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Showing 1 - 200 of 1205 Journals sorted alphabetically
3 Biotech     Open Access   (Followers: 7)
3D Research     Hybrid Journal   (Followers: 19)
AAPG Bulletin     Full-text available via subscription   (Followers: 5)
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Abstract and Applied Analysis     Open Access   (Followers: 3)
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ACS Nano     Full-text available via subscription   (Followers: 215)
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Acta Metallurgica Sinica (English Letters)     Hybrid Journal   (Followers: 5)
Acta Polytechnica : Journal of Advanced Engineering     Open Access   (Followers: 2)
Acta Scientiarum. Technology     Open Access   (Followers: 3)
Acta Universitatis Cibiniensis. Technical Series     Open Access  
Active and Passive Electronic Components     Open Access   (Followers: 7)
Adaptive Behavior     Hybrid Journal   (Followers: 10)
Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi     Open Access  
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American Journal of Engineering Education     Open Access   (Followers: 9)
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American Journal of Industrial and Business Management     Open Access   (Followers: 23)
Analele Universitatii Ovidius Constanta - Seria Chimie     Open Access  
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
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Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
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at - Automatisierungstechnik     Hybrid Journal   (Followers: 1)
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Australasian Physical & Engineering Sciences in Medicine     Hybrid Journal   (Followers: 1)
Australian Journal of Multi-Disciplinary Engineering     Full-text available via subscription   (Followers: 2)
Autonomous Mental Development, IEEE Transactions on     Hybrid Journal   (Followers: 7)
Avances en Ciencias e Ingeniería     Open Access  
Balkan Region Conference on Engineering and Business Education     Open Access   (Followers: 1)
Bangladesh Journal of Scientific and Industrial Research     Open Access  
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Beni-Suef University Journal of Basic and Applied Sciences     Open Access   (Followers: 3)
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Bharatiya Vaigyanik evam Audyogik Anusandhan Patrika (BVAAP)     Open Access   (Followers: 1)
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Biomedical Engineering Letters     Hybrid Journal   (Followers: 5)
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Biomedizinische Technik - Biomedical Engineering     Hybrid Journal  
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Biotechnology Progress     Hybrid Journal   (Followers: 39)
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Boundary Value Problems     Open Access   (Followers: 1)
Brazilian Journal of Science and Technology     Open Access   (Followers: 2)
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Bulletin of Canadian Petroleum Geology     Full-text available via subscription   (Followers: 14)
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Cahiers, Droit, Sciences et Technologies     Open Access  
Calphad     Hybrid Journal  
Canadian Geotechnical Journal     Full-text available via subscription   (Followers: 13)
Canadian Journal of Remote Sensing     Full-text available via subscription   (Followers: 40)
Case Studies in Engineering Failure Analysis     Open Access   (Followers: 7)
Case Studies in Thermal Engineering     Open Access   (Followers: 3)
Catalysis Communications     Hybrid Journal   (Followers: 6)
Catalysis Letters     Hybrid Journal   (Followers: 2)
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Catalysis Science and Technology     Free   (Followers: 6)
Catalysis Surveys from Asia     Hybrid Journal   (Followers: 3)
Catalysis Today     Hybrid Journal   (Followers: 5)
CEAS Space Journal     Hybrid Journal  
Cellular and Molecular Neurobiology     Hybrid Journal   (Followers: 3)
Central European Journal of Engineering     Hybrid Journal   (Followers: 1)
CFD Letters     Open Access   (Followers: 6)
Chaos : An Interdisciplinary Journal of Nonlinear Science     Hybrid Journal   (Followers: 2)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Engineering     Open Access   (Followers: 2)
Chinese Science Bulletin     Open Access   (Followers: 1)
Ciencia e Ingenieria Neogranadina     Open Access  
Ciencia en su PC     Open Access   (Followers: 1)
Ciencias Holguin     Open Access   (Followers: 1)
CienciaUAT     Open Access  
Cientifica     Open Access  
CIRP Annals - Manufacturing Technology     Full-text available via subscription   (Followers: 11)
CIRP Journal of Manufacturing Science and Technology     Full-text available via subscription   (Followers: 14)
City, Culture and Society     Hybrid Journal   (Followers: 21)
Clay Minerals     Full-text available via subscription   (Followers: 9)
Clean Air Journal     Full-text available via subscription   (Followers: 2)
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Cogent Engineering     Open Access   (Followers: 2)
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Color Research & Application     Hybrid Journal   (Followers: 1)
COMBINATORICA     Hybrid Journal  
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Combustion, Explosion, and Shock Waves     Hybrid Journal   (Followers: 13)
Communications Engineer     Hybrid Journal   (Followers: 1)
Communications in Numerical Methods in Engineering     Hybrid Journal   (Followers: 2)
Components, Packaging and Manufacturing Technology, IEEE Transactions on     Hybrid Journal   (Followers: 23)
Composite Interfaces     Hybrid Journal   (Followers: 6)
Composite Structures     Hybrid Journal   (Followers: 252)
Composites Part A : Applied Science and Manufacturing     Hybrid Journal   (Followers: 176)
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Corrosion Science     Hybrid Journal   (Followers: 24)
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CTheory     Open Access  

        1 2 3 4 5 6 | Last

Journal Cover Applied Numerical Mathematics
  [SJR: 1.254]   [H-I: 56]   [5 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0168-9274 - ISSN (Online) 0168-9274
   Published by Elsevier Homepage  [3031 journals]
  • An error estimate for an energy conserving spectral scheme approximating
           the dynamic elastica with free ends
    • Authors: Kazuho Ito
      Pages: 1 - 20
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Kazuho Ito
      An energy conserving spectral scheme is presented for approximating the smooth solution of the dynamic elastica with free ends. The spatial discretization of the elastica is done on the basis of Galerkin spectral methods with a Legendre grid. It is established that the scheme has the unique solution and enjoys a spectral accuracy with respect to the size of the spatial grid. Moreover, some results of a numerical simulation are given to verify that the implemented scheme preserves the discrete energy.

      PubDate: 2017-05-13T08:01:38Z
      DOI: 10.1016/j.apnum.2017.05.001
      Issue No: Vol. 120 (2017)
  • Unconditional error estimates for time dependent viscoelastic fluid flow
    • Authors: Haibiao Zheng; Jiaping Yu; Li Shan
      Pages: 1 - 17
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Haibiao Zheng, Jiaping Yu, Li Shan
      The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.010
      Issue No: Vol. 119 (2017)
  • A numerical method for solving the time variable fractional order
           mobile–immobile advection–dispersion model
    • Authors: Wei Jiang; Na Liu
      Pages: 18 - 32
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Wei Jiang, Na Liu
      In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile–immobile advection–dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection–dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order γ ( x , t ) ∈ [ 0 , 1 ] . In order to solve this kind of equation, we discuss and derive the ε-approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.014
      Issue No: Vol. 119 (2017)
  • Difference schemes for systems of second order nonlinear ODEs on a
           semi-infinite interval
    • Authors: M. Król; M.V. Kutniv; O.I. Pazdriy
      Pages: 33 - 50
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): M. Król, M.V. Kutniv, O.I. Pazdriy
      The three-point difference schemes of high order accuracy for the numerical solving boundary value problems on a semi-infinite interval for systems of second order nonlinear ordinary differential equations with a not self-conjugate operator are constructed and justified. We proved the existence and uniqueness of solutions of the three-point difference schemes and obtained the estimate of their accuracy. The results of numerical experiments which confirm the theoretical results are given.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.012
      Issue No: Vol. 119 (2017)
  • Spectral element technique for nonlinear fractional evolution equation,
           stability and convergence analysis
    • Authors: Mehdi Dehghan; Mostafa Abbaszadeh
      Pages: 51 - 66
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Mehdi Dehghan, Mostafa Abbaszadeh
      In the current manuscript, we consider a fractional partial integro-differential equation that is called fractional evolution equation. The fractional evolution equation is based on the Riemann–Liouville fractional integral. The presented numerical algorithm is based on the following procedures: at first a difference scheme has been used to discrete the temporal direction and secondly the spectral element method is applied to discrete the spatial direction and finally these procedures are combined to obtain a full-discrete scheme. For the constructed numerical technique, we prove the unconditional stability and also obtain an error bound. We use the energy method to analysis the full-discrete scheme. We employ some test problems to show the high accuracy of the proposed technique. Also, we compare the obtained numerical results using the present method with the existing methods in the literature.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.03.009
      Issue No: Vol. 119 (2017)
  • Highly symmetric 3-refinement Bi-frames for surface multiresolution
    • Authors: Qingtang Jiang; Dale K. Pounds
      Pages: 1 - 18
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Qingtang Jiang, Dale K. Pounds
      Multiresolution techniques for (mesh-based) surface processing have been developed and successfully used in surface progressive transmission, compression and other applications. A triangular mesh allows 3 , dyadic and 7 refinements. The 3 -refinement is the most appealing one for multiresolution data processing since it has the slowest progression through scale and provides more resolution levels within a limited capacity. The 3 refinement has been used for surface subdivision and for discrete global grid systems. Recently lifting scheme-based biorthogonal bivariate wavelets with high symmetry have been constructed for surface multiresolution processing. If biorthogonal wavelets (with either dyadic or 3 refinement) have certain smoothness, they will have big supports. In other words, the corresponding multiscale algorithms have large templates; and this is undesirable for surface processing. On the other hand, frames provide a flexibility for the construction of system generators (called framelets) with high symmetry and smaller supports. In this paper we study highly symmetric 3 -refinement wavelet bi-frames for surface processing. We design the frame algorithms based on the vanishing moments and smoothness of the framelets. The frame algorithms obtained in this paper are given by templates so that one can easily implement them. We also present interpolatory 3 subdivision-based frame algorithms. In addition, we provide frame ternary multiresolution algorithms for boundary vertices on an open surface.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.005
      Issue No: Vol. 118 (2017)
  • Numerical study of an adaptive domain decomposition algorithm based on
           Chebyshev tau method for solving singular perturbed problems
    • Authors: Wenting Shao; Xionghua Wu; Cheng Wang
      Pages: 19 - 32
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Wenting Shao, Xionghua Wu, Cheng Wang
      It is known that spectral methods offer exponential convergence for infinitely smooth solutions. However, they are not applicable for problems presenting singularities or thin layers, especially true for the ones with the location of singularity unknown. An adaptive domain decomposition method (DDM) integrated with Chebyshev tau method based on the highest derivative (CTMHD) is introduced to solve singular perturbed boundary value problems (SPBVPs). The proposed adaptive algorithm uses the refinement indicators based on Chebyshev coefficients to determine which subintervals need to be refined. Numerical experiments have been conducted to demonstrate the superior performance of the method for SPBVPs with a number of singularities including boundary layers, interior layers and dense oscillations. A fourth order nonlinear SPBVP is also concerned. The numerical results illustrate the efficiency and applicability of our adaptive algorithm to capture the locations of singularities, and the higher accuracy in comparison with some existing numerical methods in the literature.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.006
      Issue No: Vol. 118 (2017)
  • Spectral discretization of the Navier–Stokes problem with mixed
           boundary conditions
    • Authors: Yasmina Daikh; Driss Yakoubi
      Pages: 33 - 49
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Yasmina Daikh, Driss Yakoubi
      We consider a variational formulation of the three dimensional Navier–Stokes equations provided with mixed boundary conditions. We write this formulation with three independent unknowns: the vorticity, the velocity and the pressure. Next, we propose a discretization by spectral methods. A detailed numerical analysis leads to a priori error estimates for the three unknowns.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.002
      Issue No: Vol. 118 (2017)
  • Weak stochastic Runge–Kutta Munthe-Kaas methods for finite spin
    • Authors: M. Ableidinger; E. Buckwar
      Pages: 50 - 63
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): M. Ableidinger, E. Buckwar
      In this article we construct weak Runge–Kutta Munthe-Kaas methods for a finite-dimensional version of the stochastic Landau–Lifshitz equation (LL-equation). We formulate a Lie group framework for the stochastic LL-equation and derive regularity conditions for the corresponding SDE system on the Lie algebra. Using this formulation we define weak Munthe-Kaas methods based on weak stochastic Runge–Kutta methods (SRK methods) and provide sufficient conditions such that the Munthe-Kaas methods inherit the convergence order of the underlying SRK method. The constructed methods are fully explicit and preserve the norm constraint of the LL-equation exactly. Numerical simulations are provided to illustrate the convergence order as well as the long time behaviour of the proposed methods.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.01.017
      Issue No: Vol. 118 (2017)
  • Analysis of order reduction when integrating linear initial boundary value
           problems with Lawson methods
    • Authors: I. Alonso-Mallo; B. Cano; N. Reguera
      Pages: 64 - 74
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): I. Alonso-Mallo, B. Cano, N. Reguera
      In this paper, a thorough analysis is given for the order which is observed when integrating evolutionary linear partial differential equations with Lawson methods. The analysis is performed under the general framework of C0-semigroups in Banach spaces and hence it can be applied to the numerical time integration of many initial boundary value problems which are described by linear partial differential equations. Conditions of regularity and annihilation at the boundary of these problems are then stated to justify the precise order which is observed, including fractional order of convergence.

      PubDate: 2017-03-03T19:08:30Z
      DOI: 10.1016/j.apnum.2017.02.010
      Issue No: Vol. 118 (2017)
  • An efficient two-level finite element algorithm for the natural convection
    • Authors: Pengzhan Huang
      Pages: 75 - 86
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Pengzhan Huang
      An efficient two-level finite element algorithm for solving the natural convection equations is developed and studied in this paper. By solving one small nonlinear system on a coarse mesh H and two large linearized problems on a fine mesh h = O ( H 7 − ε 2 ) with different loads, we can obtain an approximation solution ( u h , p h , T h ) with the convergence rate of same order as the usual finite element solution, which involves one large nonlinear natural convection system on the same fine mesh h. Furthermore, compared with the results of Si's algorithm in 2011, the given algorithm costs less computed time to get almost the same precision.

      PubDate: 2017-03-09T19:12:42Z
      DOI: 10.1016/j.apnum.2017.02.012
      Issue No: Vol. 118 (2017)
  • High-order numerical solution of the Helmholtz equation for domains with
           reentrant corners
    • Authors: S. Magura; S. Petropavlovsky; S. Tsynkov; E. Turkel
      Pages: 87 - 116
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): S. Magura, S. Petropavlovsky, S. Tsynkov, E. Turkel
      Standard numerical methods often fail to solve the Helmholtz equation accurately near reentrant corners, since the solution may become singular. The singularity has an inhomogeneous contribution from the boundary data near the corner and a homogeneous contribution that is determined by boundary conditions far from the corner. We present a regularization algorithm that uses a combination of analytical and numerical tools to distinguish between these two contributions and ultimately subtract the singularity. We then employ the method of difference potentials to numerically solve the regularized problem with high-order accuracy over a domain with a curvilinear boundary. Our numerical experiments show that the regularization successfully restores the design rate of convergence.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.02.013
      Issue No: Vol. 118 (2017)
  • Galerkin finite element method for the nonlinear fractional
           Ginzburg–Landau equation
    • Authors: Meng Li; Chengming Huang; Nan Wang
      Pages: 131 - 149
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Meng Li, Chengming Huang, Nan Wang
      In this paper, we are concerned with the numerical solution of the nonlinear fractional Ginzburg–Landau equation. Galerkin finite element method is used for the spatial discretization, and an implicit midpoint difference method is employed for the temporal discretization. The boundedness, existence and uniqueness of the numerical solution, and the unconditional error estimates in the L 2 -norm are investigated in details. To numerically solve the nonlinear system, linearized iterative algorithms are also considered. Finally, some numerical examples are presented to illustrate the effectiveness of the algorithm.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.003
      Issue No: Vol. 118 (2017)
  • Design and evaluation of homotopies for efficient and robust continuation
    • Authors: David A. Brown; David W. Zingg
      Pages: 150 - 181
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): David A. Brown, David W. Zingg
      Homotopy continuation, in combination with a quasi-Newton method, can be an efficient and robust technique for solving large sparse systems of nonlinear equations. The homotopy itself is pivotal in determining the efficiency and robustness of the continuation algorithm. As the homotopy is defined implicitly by a nonlinear system of equations to which the analytical solution is by assumption unknown, many properties of the homotopy can only be studied using numerical methods. The properties of a given homotopy which have the greatest impact on the corresponding continuation algorithm are traceability and linear solver performance. Metrics are presented for the analysis and characterization of these properties. Several homotopies are presented and studied using these metrics in the context of a parallel implicit three-dimensional Newton–Krylov–Schur flow solver for computational fluid dynamics. Several geometries, grids, and flow types are investigated in the study. Additional studies include the impact of grid refinement and the application of a coordinate transformation to the homotopy as measured through the traceability and linear solver performance metrics.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.001
      Issue No: Vol. 118 (2017)
  • Analysis of output-based error estimation for finite element methods
    • Authors: Hugh A. Carson; David L. Darmofal; Marshall C. Galbraith; Steven R. Allmaras
      Pages: 182 - 202
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Hugh A. Carson, David L. Darmofal, Marshall C. Galbraith, Steven R. Allmaras
      In this paper, we develop a priori estimates for the convergence of outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Output error estimates for order p finite element solutions are constructed using the Dual-Weighted Residual (DWR) method with a higher-order p ′ > p dual solution. Specifically, we analyze these DWR estimates for Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods applied to the Poisson problem. For all discretizations, as h → 0 , we prove that the output and output error estimate converge at order 2p and 2 p ′ (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2 p + d and p + p ′ + d . For DG, the results use a new post processing for the error associated with the lifting operator. For HDG, these rates improve an additional order when the stabilization is based upon an O ( 1 ) length scale.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.004
      Issue No: Vol. 118 (2017)
  • On fractional backward differential formulas for fractional delay
           differential equations with periodic and anti-periodic conditions
    • Authors: M. Saedshoar Heris; M. Javidi
      Pages: 203 - 220
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): M. Saedshoar Heris, M. Javidi
      In this paper, fractional backward differential formulas (FBDF) are presented for the numerical solution of fractional delay differential equations (FDDEs) of the form λ n 0 C D t α n y ( t ) + λ n − 1 0 C D t α n − 1 y ( t ) + ⋯ + λ 1 0 C D t α 1 y ( t ) + λ n + 1 y ( t − τ ) = f ( t ) , t ∈ [ 0 , T ] , where λ i ∈ R ( i = 1 , ⋯ , n + 1 ) , λ n + 1 ≠ 0 , 0 ⩽ α 1 < α 2 < ⋯ < α n < 1 , T > 0 , in Caputo sense. Our investigation is focused on stability properties of the numerical methods and we determine stability regions for the FDDEs. Also we find the Green's functions for this equation corresponding to periodic/anti-periodic conditions in terms of the functions of Mittag Leffler type. Numerical tests are presented to confirm the strength of the approach under investigation.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.03.006
      Issue No: Vol. 118 (2017)
  • IMEX peer methods for fast-wave–slow-wave problems
    • Authors: Behnam Soleimani; Oswald Knoth; Rüdiger Weiner
      Pages: 221 - 237
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Behnam Soleimani, Oswald Knoth, Rüdiger Weiner
      Differential equations with both stiff and nonstiff parts can be solved efficiently by implicit–explicit (IMEX) methods. There have been considered various approaches in the literature. In this paper we introduce IMEX peer methods. We show that the combination of s-stage explicit and implicit peer methods, both of order p, gives an IMEX peer method of the same order. We construct methods of order p = s for s = 3 , 4 , where we compute the free parameters numerically to give good stability with respect to fast-wave–slow-wave problems from weather prediction. We implement these methods with and without step size control. Tests and comparisons with other methods for problems mostly from weather prediction show the high potential of IMEX peer methods.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.02.016
      Issue No: Vol. 118 (2017)
  • Analysis of a group finite element formulation
    • Authors: Gabriel R. Barrenechea; Petr Knobloch
      Pages: 238 - 248
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Gabriel R. Barrenechea, Petr Knobloch
      The group finite element formulation is a strategy aimed at speeding the assembly of finite element matrices for time-dependent problems. This process modifies the Galerkin matrix of the problem in a non-consistent way. This may cause a deterioration of both the stability and convergence of the method. In this paper we prove results for a group finite element formulation of a convection–diffusion–reaction equation showing that the stability of the original discrete problem remains unchanged under appropriate conditions on the data of the problem and on the discretization parameters. A violation of these conditions may lead to non-existence of solutions, as one of our main results shows. An analysis of the consistency error introduced by the group finite element formulation and its skew-symmetric variant is given.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.008
      Issue No: Vol. 118 (2017)
  • Analysis of non-negativity and convergence of solution of the balanced
           implicit method for the delay Cox–Ingersoll–Ross model
    • Authors: A.S. Fatemion Aghda; Seyed Mohammad Hosseini; Mahdieh Tahmasebi
      Pages: 249 - 265
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): A.S. Fatemion Aghda, Seyed Mohammad Hosseini, Mahdieh Tahmasebi
      The delay Cox–Ingersoll–Ross (CIR) model is an important model in the financial markets. It has been proved that the solution of this model is non-negative and its pth moments are bounded. However, there is no explicit solution for this model. So, proposing appropriate numerical method for solving this model which preserves non-negativity and boundedness of the model's solution is very important. In this paper, we concentrate on the balanced implicit method (BIM) for this model and show that with choosing suitable control functions the BIM provides numerical solution that preserves non-negativity of solution of the model. Moreover, we show the pth moment boundedness of the numerical solution of the method and prove the convergence of the proposed numerical method. Finally, we present some numerical examples to confirm the theoretical results, and also application of BIM to compute some financial quantities.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.007
      Issue No: Vol. 118 (2017)
  • BDF-type shifted Chebyshev approximation scheme for fractional functional
           differential equations with delay and its error analysis
    • Authors: V.G. Pimenov; A.S. Hendy
      Pages: 266 - 276
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): V.G. Pimenov, A.S. Hendy
      A numerical method for fractional order differential equations (FDEs) and constant or time-varying delayed fractional differential equations (FDDEs) is constructed. This method is of BDF-type which is based on the interval approximation of the true solution by truncated shifted Chebyshev series. This approach can be reformulated in an equivalent way as a Runge–Kutta method and its Butcher tableau is given. A detailed local and global truncating errors analysis is deduced for the numerical solutions of FDEs and FDDEs. Illustrative examples are included to demonstrate the validity and applicability of the proposed approach.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.013
      Issue No: Vol. 118 (2017)
  • Quadrature rules and asymptotic expansions for two classes of oscillatory
           Bessel integrals with singularities of algebraic or logarithmic type
    • Authors: Hongchao Kang; Junjie Ma
      Pages: 277 - 291
      Abstract: Publication date: August 2017
      Source:Applied Numerical Mathematics, Volume 118
      Author(s): Hongchao Kang, Junjie Ma
      In this paper we mainly focus on the quadrature rules and asymptotic expansions for two classes of highly oscillatory Bessel integrals with algebraic or logarithmic singularities. Firstly, by two transformations, we transfer them into the standard types on [ − 1 , 1 ] , and derive two useful asymptotic expansions in inverse powers of the frequency ω. Then, based on the two asymptotic expansions, two methods are presented, respectively. One is the so-called Filon-type method. The other is the more efficient Clenshaw-Curtis–Filon-type method, which can be implemented in O ( N log ⁡ N ) operations, based on Fast Fourier Transform (FFT) and fast computation of the modified moments. Here, through large amount of calculation and analysis, we can construct two important recurrence relations for computing the modified moments accurately, based on the Bessel's equation and some properties of the Chebyshev polynomials. In particular, we also provide error analysis for these methods in inverse powers of the frequency ω. Furthermore, we prove directly from the presented error bounds that these methods share the advantageous property, that the larger the values of the frequency ω, the higher the accuracy. The efficiency and accuracy of the proposed methods are illustrated by numerical examples.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.011
      Issue No: Vol. 118 (2017)
  • Parallel finite element variational multiscale algorithms for
           incompressible flow at high Reynolds numbers
    • Authors: Yueqiang Shang; Jin Qin
      Pages: 1 - 21
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): Yueqiang Shang, Jin Qin
      Based on two-grid discretizations, some parallel finite element variational multiscale algorithms for the steady incompressible Navier–Stokes equations at high Reynolds numbers are presented and compared. In these algorithms, a stabilized Navier–Stokes system is first solved on a coarse grid, and then corrections are calculated independently on overlapped fine grid subdomains by solving a local stabilized linear problem. The stabilization terms for the coarse and fine grid problems are based on two local Gauss integrations. Error bounds for the approximate solution are estimated. Algorithmic parameter scalings are also derived. The theoretical results show that, with suitable scalings of the algorithmic parameters, these algorithms can yield an optimal rate of convergence. Numerical results are given to verify the theoretical predictions and demonstrate the effectiveness of the proposed algorithms.

      PubDate: 2017-02-11T18:09:57Z
      DOI: 10.1016/j.apnum.2017.01.018
      Issue No: Vol. 117 (2017)
  • A posteriori error estimation for multi-stage Runge–Kutta IMEX
    • Authors: Jehanzeb H. Chaudhry; J.B. Collins; John N. Shadid
      Pages: 36 - 49
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): Jehanzeb H. Chaudhry, J.B. Collins, John N. Shadid
      Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. The use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error in a quantity-of-interest.

      PubDate: 2017-02-24T19:03:59Z
      DOI: 10.1016/j.apnum.2017.01.021
      Issue No: Vol. 117 (2017)
  • Fully-geometric mesh one-leg methods for the generalized pantograph
           equation: Approximating Lyapunov functional and asymptotic contractivity
    • Authors: Wansheng Wang
      Pages: 50 - 68
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): Wansheng Wang
      Motivated by recent stability results on one-step methods, especially Runge–Kutta methods, for the generalized pantograph equation (GPE), in this paper we study the stability of one-leg multistep methods for these equations since the one-leg methods have less computational cost than Runge–Kutta methods. To do this, a new stability concept, G q ( q ¯ ) -stability defined for variable stepsizes one-leg methods with the stepsize ratio q which is an extension of G-stability defined for constant stepsizes one-leg methods, is introduced. The Lyapunov functional of linear system is obtained and numerically approximated. It is proved that a G q ( q ¯ ) -stable fully-geometric mesh one-leg method can preserve the decay property of the Lyapunov functional for any q ∈ [ 1 , q ¯ ] . The asymptotic contractivity, a new stability concept at vanishing initial interval, is introduced for investigating the effect of the initial interval approximation on the stability of numerical solutions. This property and the bounded stability of G q ( q ¯ ) -stable one-leg methods for linear and nonlinear problems are analyzed. A numerical example which further illustrates our theoretical results is provided.

      PubDate: 2017-02-24T19:03:59Z
      DOI: 10.1016/j.apnum.2017.01.019
      Issue No: Vol. 117 (2017)
  • Partitioned general linear methods for separable Hamiltonian problems
    • Authors: John C. Butcher; Raffaele D'Ambrosio
      Pages: 69 - 86
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): John C. Butcher, Raffaele D'Ambrosio
      Partitioned general linear methods possessing the G-symplecticity property are introduced. These are intended for the numerical solution of separable Hamiltonian problems and, as for multivalue methods in general, there is a potential for loss of accuracy because of parasitic solution growth. The solution of mechanical problems over extended time intervals often benefits from interchange symmetry as well as from symplectic behaviour. A special type of symmetry, known as interchange symmetry, is developed from a model Runge–Kutta case to a full multivalue case. Criteria are found for eliminating parasitic behaviour and order conditions are explored.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.02.001
      Issue No: Vol. 117 (2017)
  • Filon–Clenshaw–Curtis formulas for highly oscillatory integrals in the
           presence of stationary points
    • Authors: Hassan Majidian
      Pages: 87 - 102
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): Hassan Majidian
      Numerical approximation of a general class of one-dimensional highly oscillatory integrals over bounded intervals with exponential oscillators is considered. A Filon-type method based on modified Clenshaw–Curtis quadrature rules is developed and its stability is established when the stationary points of the oscillator function are all of order two. Also, an error estimate for the method is provided, which shows that the method is convergent as the number of Clenshaw–Curtis points increases, and the rate of convergence depends only on the Sobolev regularity of the integrand. Using some numerical experiments, the theoretical results are illustrated.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.02.003
      Issue No: Vol. 117 (2017)
  • Delay-dependent stability of symmetric Runge–Kutta methods for second
           order delay differential equations with three parameters
    • Authors: Jingjun Zhao; Yan Fan; Yang Xu
      Pages: 103 - 114
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): Jingjun Zhao, Yan Fan, Yang Xu
      The paper is concerned with the delay-dependent stability analysis of symmetric Runge–Kutta methods, which include the Gauss methods and the Lobatto IIIA, IIIB and IIIS methods, for the second order delay differential equations with three parameters. By using the root locus technique, the root locus curve is given and the numerical stability region of symmetric Runge–Kutta methods is obtained. It is proved that, under some conditions, the analytical stability region is contained in the numerical stability region. Numerical examples confirming the theoretical results are presented.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.03.005
      Issue No: Vol. 117 (2017)
  • Two-dimensional Shannon wavelet inverse Fourier technique for pricing
           European options
    • Authors: G. Colldeforns-Papiol; L. Ortiz-Gracia; C.W. Oosterlee
      Pages: 115 - 138
      Abstract: Publication date: July 2017
      Source:Applied Numerical Mathematics, Volume 117
      Author(s): G. Colldeforns-Papiol, L. Ortiz-Gracia, C.W. Oosterlee
      The SWIFT method for pricing European-style options on one underlying asset was recently published and presented as an accurate, robust and highly efficient technique. The purpose of this paper is to extend the method to higher dimensions by pricing exotic option contracts, called rainbow options, whose payoff depends on multiple assets. The multidimensional extension inherits the properties of the one-dimensional method, being the exponential convergence one of them. Thanks to the nature of local Shannon wavelets basis, we do not need to rely on a-priori truncation of the integration range, we have an error bound estimate and we use fast Fourier transform (FFT) algorithms to speed up computations. We test the method for similar examples with state-of-the-art methods found in the literature, and we compare our results with analytical expressions when available.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.03.002
      Issue No: Vol. 117 (2017)
  • Special issue on New Trends in Numerical Analysis: Theory, Methods,
           Algorithms and Applications (NETNA2015)
    • Authors: Francesco Dell'Accio; Maria Italia Gualtieri; Stefano Serra Capizzano; Gerhard Wanner
      First page: 1
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Francesco Dell'Accio, Maria Italia Gualtieri, Stefano Serra Capizzano, Gerhard Wanner

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.02.007
      Issue No: Vol. 116 (2017)
  • Matrix approach to hypercomplex Appell polynomials
    • Authors: Lidia Aceto; Helmut Robert Malonek; Graça Tomaz
      Pages: 2 - 9
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Lidia Aceto, Helmut Robert Malonek, Graça Tomaz
      Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a suitable first order initial value problem. The paper aims to confirm that the unifying character of this approach can also be applied to the construction of homogeneous Appell polynomials that are solutions of a generalized Cauchy–Riemann system in Euclidean spaces of arbitrary dimension. The result contributes to the development of techniques for polynomial approximation and interpolation in non-commutative Hypercomplex Function Theories with Clifford algebras.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.006
      Issue No: Vol. 116 (2017)
  • Non-polynomial spline alternatives in Isogeometric Symmetric Galerkin BEM
    • Authors: A. Aimi; M. Diligenti; M.L. Sampoli; A. Sestini
      Pages: 10 - 23
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): A. Aimi, M. Diligenti, M.L. Sampoli, A. Sestini
      The application of the Isogeometric Analysis (IgA) paradigm to Symmetric Galerkin Boundary Element Method (SGBEM) is investigated. In order to obtain a very flexible approach, the study is here developed by using non-polynomial spline functions to represent both the domain boundary and the approximate solution. The numerical comparison between IGA-SGBEM and both curvilinear and standard SGBEM approaches shows the general capability of the presented method to produce accurate approximate solutions with less degrees of freedom.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.004
      Issue No: Vol. 116 (2017)
  • Shift techniques for Quasi-Birth and Death processes: Canonical
           factorizations and matrix equations
    • Authors: D.A. Bini; G. Latouche; B. Meini
      Pages: 24 - 36
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): D.A. Bini, G. Latouche, B. Meini
      We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes He et al. (2001) [13] in functional form by bringing the attention to the existence and properties of canonical factorizations. To this regard, we prove new results concerning the solutions of the quadratic matrix equations associated with the QBD. These results find applications to the solution of the Poisson equation for QBDs.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.09.001
      Issue No: Vol. 116 (2017)
  • Efficient cyclic reduction for Quasi-Birth–Death problems with rank
           structured blocks
    • Authors: Dario A. Bini; Stefano Massei; Leonardo Robol
      Pages: 37 - 46
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Dario A. Bini, Stefano Massei, Leonardo Robol
      We provide effective algorithms for solving block tridiagonal block Toeplitz systems with m × m quasiseparable blocks, as well as quadratic matrix equations with m × m quasiseparable coefficients, based on cyclic reduction and on the technology of rank-structured matrices. The algorithms rely on the exponential decay of the singular values of the off-diagonal submatrices generated by cyclic reduction. We provide a formal proof of this decay in the Markovian framework. The results of the numerical experiments that we report confirm a significant speed up over the general algorithms, already starting with the moderately small size m ≈ 10 2 .

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.06.014
      Issue No: Vol. 116 (2017)
  • Polynomial approximation on Lissajous curves in the d-cube
    • Authors: L. Bos; S. De Marchi; M. Vianello
      Pages: 47 - 56
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): L. Bos, S. De Marchi, M. Vianello
      For a ∈ Z > 0 d we let ℓ a ( t ) : = ( cos ⁡ ( a 1 t ) , cos ⁡ ( a 2 t ) , ⋯ , cos ⁡ ( a d t ) ) denote an associated Lissajous curve. We study such Lissajous curves which have the quadrature property for the cube [ − 1 , 1 ] d that ∫ [ − 1 , 1 ] d p ( x ) d μ d ( x ) = 1 π ∫ 0 π p ( ℓ a ( t ) ) d t for all polynomials p ( x ) ∈ V where V is either the space of d-variate polynomials of degree at most m or else the d-fold tensor product of univariate polynomials of degree at most m. Here d μ d is the product Chebyshev measure (also the pluripotential equilibrium measure for the cube). Among such Lissajous curves with this property we study the ones for which max p ∈ V ⁡ deg ( p ( ℓ a ( t ) ) ) is as small as possible. In the tensor product case we show that this is uniquely minimized by g : = ( 1 , ( m + 1 ) , ( m + 1 ) 2 , ⋯ , ( m + 1 ) d − 1 ) . In the case of m = 2 n we construct discrete hyperinterpolation formulas which are easily evaluated with, for example, the Chebfun system ([6]).

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.01.013
      Issue No: Vol. 116 (2017)
  • Shanks function transformations in a vector space
    • Authors: Claude Brezinski; Michela Redivo-Zaglia
      Pages: 57 - 63
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Claude Brezinski, Michela Redivo-Zaglia
      In this paper, we show how to construct various extensions of Shanks transformation for functions in a vector space. They are aimed at transforming a function tending slowly to its limit when the argument tends to infinity into another function with better convergence properties. Their expressions as ratio of determinants and recursive algorithms for their implementation are given. A simplified form of one of them is derived. It allows us to obtain a convergence result for an important class of functions. An application to integrable systems is discussed.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.06.013
      Issue No: Vol. 116 (2017)
  • Regularizing preconditioners by non-stationary iterated Tikhonov with
           general penalty term
    • Authors: Alessandro Buccini
      Pages: 64 - 81
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Alessandro Buccini
      The nonstationary preconditioned iteration proposed in a recent work by Donatelli and Hanke appeared on IP can be seen as an approximated iterated Tikhonov method. Starting from this observation we extend the previous iteration in two directions: the introduction of a regularization operator different from the identity (e.g., a differential operator) and the projection into a convex set (e.g., the nonnegative cone). Depending on the application both generalizations can lead to an improvement in the quality of the computed approximations. Convergence results and regularization properties of the proposed iterations are proved. Finally, the new methods are applied to image deblurring problems and compared with the iteration in the original work and other methods with similar properties recently proposed in the literature.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.009
      Issue No: Vol. 116 (2017)
  • Numerical solution of time fractional diffusion systems
    • Authors: Kevin Burrage; Angelamaria Cardone; Raffaele D'Ambrosio; Beatrice Paternoster
      Pages: 82 - 94
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Kevin Burrage, Angelamaria Cardone, Raffaele D'Ambrosio, Beatrice Paternoster
      In this paper a general class of diffusion problem is considered, where the standard time derivative is replaced by a fractional one. For the numerical solution, a mixed method is proposed, which consists of a finite difference scheme through space and a spectral collocation method through time. The spectral method considerably reduces the computational cost with respect to step-by-step methods to discretize the fractional derivative. Some classes of spectral bases are considered, which exhibit different convergence rates and some numerical results based on time diffusion reaction diffusion equations are given.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.02.004
      Issue No: Vol. 116 (2017)
  • Partition of unity interpolation using stable kernel-based techniques
    • Authors: R. Cavoretto; S. De Marchi; A. De Rossi; E. Perracchione; G. Santin
      Pages: 95 - 107
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): R. Cavoretto, S. De Marchi, A. De Rossi, E. Perracchione, G. Santin
      In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.005
      Issue No: Vol. 116 (2017)
  • Convergence rates of derivatives of Floater–Hormann interpolants for
           well-spaced nodes
    • Authors: Emiliano Cirillo; Kai Hormann; Jean Sidon
      Pages: 108 - 118
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Emiliano Cirillo, Kai Hormann, Jean Sidon
      Floater–Hormann interpolants constitute a family of barycentric rational interpolants which are based on blending local polynomial interpolants of degree d. Recent results suggest that the k-th derivatives of these interpolants converge at the rate of O ( h d + 1 − k ) for k ≤ d as the mesh size h converges to zero. So far, this convergence rate has been proven for k = 1 , 2 and for k ≥ 3 under the assumption of equidistant or quasi-equidistant interpolation nodes. In this paper we extend these results and prove that Floater–Hormann interpolants and their derivatives converge at the rate of O ( h j d + 1 − k ) , where h j is the local mesh size, for any k ≥ 0 and any set of well-spaced nodes.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.008
      Issue No: Vol. 116 (2017)
  • Convergence of level-dependent Hermite subdivision schemes
    • Authors: Costanza Conti; Mariantonia Cotronei; Tomas Sauer
      Pages: 119 - 128
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Costanza Conti, Mariantonia Cotronei, Tomas Sauer
      Subdivision schemes are known to be useful tools for approximation and interpolation of discrete data. In this paper, we study conditions for the convergence of level-dependent Hermite subdivision schemes, which act on vector valued data interpreting their components as function values and associated consecutive derivatives. In particular, we are interested in schemes preserving spaces of polynomials and exponentials. Such preservation property assures the existence of a cancellation operator in terms of which it is possible to obtain a factorization of the subdivision operators at each level. With the help of this factorization, we provide sufficient conditions for the convergence of the scheme based on some contractivity assumptions on the associated difference scheme.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2017.02.011
      Issue No: Vol. 116 (2017)
  • A class of Birkhoff–Lagrange-collocation methods for high order
           boundary value problems
    • Authors: Francesco A. Costabile; Anna Napoli
      Pages: 129 - 140
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Francesco A. Costabile, Anna Napoli
      A general procedure to determine collocation methods for high order boundary value problems is presented. These methods provide globally continuous differentiable solution in the form of polynomial functions and also numerical solution on a set of discrete points. Some special cases are considered. Numerical experiments are presented which support theoretical results and provide favorable comparisons with other existing methods.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.12.003
      Issue No: Vol. 116 (2017)
  • Performances and limitations of the diffusive approximation of the 2-d
           shallow water equations for flood simulation in urban and rural areas
    • Authors: Pierfranco Costabile; Carmelina Costanzo; Francesco Macchione
      Pages: 141 - 156
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Pierfranco Costabile, Carmelina Costanzo, Francesco Macchione
      The Shallow Water Equations (SWE) are a time-dependent system of non-linear partial differential equations of hyperbolic type. Flood propagation in rivers and in the neighbouring areas is a typical example for which the use of the SWE is required. The numerical integration of the SWE needs complicated schemes that still require a significant computational effort. This fact has maintained interest in techniques that can approximate simulations from full two-dimensional (2-D) shallow water models with less computation heaviness. In particular, an approximation of the full SWE consists in neglecting the inertial terms, leading to a degradation of the original hyperbolic model to a parabolic one. This approximation is traditionally justified by the fact that flooding over plain areas is characterized by a slow evolution. Although there are important papers on model benchmarking and comparative analysis of flood propagation models, detailed analyses of effective ability and limitations of simplified models in reproducing floods processes are still rare, especially for urban environments. Therefore, this paper aims at providing a contribution to the model benchmarking and to the influence induced by the application of simplified models on the numerical simulations of flood events, overcoming some limitations that characterize part of the studies in the literature. In particular, on the one hand, more complicated experimental tests will be considered and, on the other hand, the same numerical grid for every model considered herein will be used in order to remove its effect from the numerical results. The simulations discussed here seem to suggest that the use of diffusive-type models is questionable, especially in urban districts, due to the poor predictions of the events that might be simulated around the buildings. Conversely, the application of the shallow water model gave excellent results in all the situations considered in this paper and, therefore, its use is recommended to obtained reliable estimations of flood hazard.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.07.003
      Issue No: Vol. 116 (2017)
  • Reconstruction of implicit curves and surfaces via RBF interpolation
    • Authors: Salvatore Cuomo; Ardelio Galletti; Giulio Giunta; Livia Marcellino
      Pages: 157 - 171
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Salvatore Cuomo, Ardelio Galletti, Giulio Giunta, Livia Marcellino
      Representation of curves and surfaces is a basic topic in computer graphic and computer aided design (CAD). In this paper we focus on theoretical and practical issues in using radial basis functions (RBF) for reconstructing implicit curves and surfaces from point clouds. We study the conditioning of the problem and give some insight on how the problem parameters and the results have to be taken in order to achieve meaningful solutions and avoid artifacts. Moreover, a strategy for decreasing the conditioning of the problem is suggested and a general framework for preconditioning and solving the problem, even for large datasets, is also provided.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.10.016
      Issue No: Vol. 116 (2017)
  • C1 quintic splines on domains enclosed by piecewise conics and numerical
           solution of fully nonlinear elliptic equations
    • Authors: Oleg Davydov; Abid Saeed
      Pages: 172 - 183
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Oleg Davydov, Abid Saeed
      We introduce bivariate C 1 piecewise quintic finite element spaces for curved domains enclosed by piecewise conics satisfying homogeneous boundary conditions, construct local bases for them using Bernstein–Bézier techniques, and demonstrate the effectiveness of these finite elements for the numerical solution of the Monge–Ampère equation over curved domains by Böhmer's method.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.10.002
      Issue No: Vol. 116 (2017)
  • Approximation of Hilbert and Hadamard transforms on (0,+∞)
    • Authors: Maria Carmela De Bonis; Donatella Occorsio
      Pages: 184 - 194
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): Maria Carmela De Bonis, Donatella Occorsio
      The authors propose a numerical method for computing Hilbert and Hadamard transforms on ( 0 , + ∞ ) by a simultaneous approximation process involving a suitable Lagrange polynomial of degree s and “truncated” Gaussian rule of order m, with s ≪ m . The proposed procedure is convergent and pointwise error estimates are given. Finally, some numerical tests confirming the theoretical error estimates are presented.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.12.001
      Issue No: Vol. 116 (2017)
  • Scattering data computation for the Zakharov–Shabat system with
           non-smooth potentials
    • Authors: L. Fermo; C. van der Mee; S. Seatzu
      Pages: 195 - 203
      Abstract: Publication date: June 2017
      Source:Applied Numerical Mathematics, Volume 116
      Author(s): L. Fermo, C. van der Mee, S. Seatzu
      In this paper we present a variant of the method for the scattering data computation for the Zakharov–Shabat system, recently proposed by the authors. The algorithm that characterizes this variant allows us to compute the scattering data also in the presence of jump discontinuities of the initial potential.

      PubDate: 2017-03-28T17:00:42Z
      DOI: 10.1016/j.apnum.2016.09.016
      Issue No: Vol. 116 (2017)
  • Optimized interface conditions in domain decomposition methods to solve
           reaction-diffusion problems with strong heterogeneity in the coefficients
           in a sectorial domain
    • Authors: Chokri Chniti
      Abstract: Publication date: Available online 7 March 2017
      Source:Applied Numerical Mathematics
      Author(s): Chokri Chniti
      The aim of this paper is to derive an appropriate second order transmission boundary conditions near the corner used in domain decomposition methods to study the reaction-diffusion problems (“ − ∇ . ( ν ( x ) ∇ . ) + η ( x ) . ”) with strong heterogeneity in the coefficients in a singular non-convex domain with Neumann and Dirichlet boundary condition. These transmission condition will be tested and compared numerically with other approaches.

      PubDate: 2017-03-09T19:12:42Z
      DOI: 10.1016/j.apnum.2017.02.015
  • Phase-field model and its splitting numerical scheme for tissue growth
    • Authors: Darae Jeong; Junseok Kim
      Abstract: Publication date: Available online 3 February 2017
      Source:Applied Numerical Mathematics
      Author(s): Darae Jeong, Junseok Kim
      We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn–Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn–Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions.

      PubDate: 2017-02-04T17:24:24Z
      DOI: 10.1016/j.apnum.2017.01.020
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