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MATHEMATICS (646 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 6)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 20)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 9)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 4)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 9)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 3)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 2)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access  
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Numerical Analysis & Computational Mathematics     Hybrid Journal   (Followers: 5)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 17)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 1)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 5)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 1)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 4)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        1 2 3 4 | Last

Journal Cover Advances in Computational Mathematics
  [SJR: 1.255]   [H-I: 44]   [15 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1572-9044 - ISSN (Online) 1019-7168
   Published by Springer-Verlag Homepage  [2335 journals]
  • Approximation by planar elastic curves
    • Authors: David Brander; Jens Gravesen; Toke Bjerge Nørbjerg
      Pages: 25 - 43
      Abstract: Abstract We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven optimization is then used to find the approximating elastic curve.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9474-z
      Issue No: Vol. 43, No. 1 (2017)
  • An improved sweeping domain decomposition preconditioner for the Helmholtz
    • Authors: Christiaan C. Stolk
      Pages: 45 - 76
      Abstract: Abstract In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries using perfectly matched layers. Simultaneous forward and backward sweeps are introduced, thereby improving the possibilities for parallellization. Finally, the method is combined with an outer two-grid iteration. The method is studied theoretically and with numerical examples. It is shown that the modifications lead to substantial decreases in computation time and memory use, so that computation times become comparable to that of the fastests methods currently in the literature for problems with up to 108 degrees of freedom.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9475-y
      Issue No: Vol. 43, No. 1 (2017)
  • Analysis and numerical solution of a Riemann-Liouville fractional
           derivative two-point boundary value problem
    • Authors: Natalia Kopteva; Martin Stynes
      Pages: 77 - 99
      Abstract: Abstract A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Riemann-Liouville fractional derivative of order 2 − δ with 0 < δ < 1. It is shown that any solution of such a problem can be expressed in terms of solutions to two associated weakly singular Volterra integral equations of the second kind. As a consequence, existence and uniqueness of a solution to the boundary value problem are proved, the structure of this solution is elucidated, and sharp bounds on its derivatives (in terms of the parameter δ) are derived. These results show that in general the first-order derivative of the solution will blow up at x = 0, so accurate numerical solution of this class of problems is not straightforward. The reformulation of the boundary problem in terms of Volterra integral equations enables the construction of two distinct numerical methods for its solution, both based on piecewise-polynomial collocation. Convergence rates for these methods are proved and numerical results are presented to demonstrate their performance.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9476-x
      Issue No: Vol. 43, No. 1 (2017)
  • A parameter choice strategy for the inversion of multiple observations
    • Authors: Christian Gerhards; Sergiy Pereverzyev; Pavlo Tkachenko
      Pages: 101 - 112
      Abstract: Abstract In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of ‘good’ parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9477-9
      Issue No: Vol. 43, No. 1 (2017)
  • Optimal configurations of lines and a statistical application
    • Authors: François Bachoc; Martin Ehler; Manuel Gräf
      Pages: 113 - 126
      Abstract: Abstract Motivated by the construction of confidence intervals in statistics, we study optimal configurations of 2 d − 1 lines in real projective space ℝℙ d−1. For small d, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of 2 d − 1 lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9478-8
      Issue No: Vol. 43, No. 1 (2017)
  • Minimal polynomial and reduced rank extrapolation methods are related
    • Authors: Avram Sidi
      Pages: 151 - 170
      Abstract: Abstract Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two polynomial methods used for accelerating the convergence of sequences of vectors {x m }. They are applied successfully in conjunction with fixed-point iterative schemes in the solution of large and sparse systems of linear and nonlinear equations in different disciplines of science and engineering. Both methods produce approximations s k to the limit or antilimit of {x m } that are of the form \(\boldsymbol {s}_{k}={\sum }^{k}_{i=0}\gamma _{i}\boldsymbol {x}_{i}\) with \({\sum }^{k}_{i=0}\gamma _{i}=1\) , for some scalars γ i . The way the two methods are derived suggests that they might, somehow, be related to each other; this has not been explored so far, however. In this work, we tackle this issue and show that the vectors \(\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}\) and \(\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}\) produced by the two methods are related in more than one way, and independently of the way the x m are generated. One of our results states that RRE stagnates, in the sense that \(\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}=\boldsymbol {s}_{k-1}^{\textit {{\tiny {RRE}}}}\) , if and only if \(\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}\) does not exist. Another result states that, when \(\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}\) exists, there holds $$\mu_{k}\boldsymbol{s}_{k}^{\textit{{\tiny{RRE}}}}=\mu_{k-1}\boldsymbol{s}_{k-1}^{\textit{{\tiny{RRE}}}}+ \nu_{k}\boldsymbol{s}_{k}^{\textit{{\tiny{MPE}}}}\quad \text{with}\quad \mu_{k}=\mu_{k-1}+\nu_{k}, $$ for some positive scalars μ k , μ k−1, and ν k that depend only on \(\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}\) , \(\boldsymbol {s}_{k-1}^{\textit {{\tiny {RRE}}}}\) , and \(\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}\) , respectively. Our results are valid when MPE and RRE are defined in any weighted inner product and the norm induced by it. They also contain as special cases the known results pertaining to the connection between the method of Arnoldi and the method of generalized minimal residuals, two important Krylov subspace methods for solving nonsingular linear systems.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9481-0
      Issue No: Vol. 43, No. 1 (2017)
  • Null space correction and adaptive model order reduction in
           multi-frequency Maxwell’s problem
    • Authors: Michal Kordy; Elena Cherkaev; Philip Wannamaker
      Pages: 171 - 193
      Abstract: Abstract A model order reduction method is developed for an operator with a non-empty null-space and applied to numerical solution of a forward multi-frequency eddy current problem using a rational interpolation of the transfer function in the complex plane. The equation is decomposed into the part in the null space of the operator, calculated exactly, and the part orthogonal to it which is approximated on a low-dimensional rational Krylov subspace. For the Maxwell’s equations the null space is related to the null space of the curl. The proposed null space correction is related to divergence correction and uses the Helmholtz decomposition. In the case of the finite element discretization with the edge elements, it is accomplished by solving the Poisson equation on the nodal elements of the same grid. To construct the low-dimensional approximation we adaptively choose the interpolating frequencies, defining the rational Krylov subspace, to reduce the maximal approximation error. We prove that in the case of an adaptive choice of shifts, the matrix spanning the approximation subspace can never become rank deficient. The efficiency of the developed approach is demonstrated by applying it to the magnetotelluric problem, which is a geophysical electromagnetic remote sensing method used in mineral, geothermal, and groundwater exploration. Numerical tests show an excellent performance of the proposed methods characterized by a significant reduction of the computational time without a loss of accuracy. The null space correction regularizes the otherwise ill-posed interpolation problem.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9482-z
      Issue No: Vol. 43, No. 1 (2017)
  • Error estimation for quadrature by expansion in layer potential evaluation
    • Authors: Ludvig af Klinteberg; Anna-Karin Tornberg
      Pages: 195 - 234
      Abstract: Abstract In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error due to nearly singular integration in the evaluation of expansion coefficients. Using a method based on contour integration and calculus of residues, the quadrature error of nearly singular integrals can be accurately estimated. This makes it possible to derive accurate estimates for the quadrature errors related to QBX, when applied to layer potentials in two and three dimensions. As examples we derive estimates for the Laplace and Helmholtz single layer potentials. These results can be used for parameter selection in practical applications.
      PubDate: 2017-02-01
      DOI: 10.1007/s10444-016-9484-x
      Issue No: Vol. 43, No. 1 (2017)
  • Families of univariate and bivariate subdivision schemes originated from
           quartic B-spline
    • Authors: Ghulam Mustafa; Rabia Hameed
      Abstract: Abstract Families of parameter dependent univariate and bivariate subdivision schemes are presented in this paper. These families are new variants of the Lane-Riesenfeld algorithm. So the subdivision algorithms consist of both refining and smoothing steps. In refining step, we use the quartic B-spline based subdivision schemes. In smoothing step, we average the adjacent points. The bivariate schemes are the non-tensor product version of our univariate schemes. Moreover, for odd and even number of smoothing steps, we get the primal and dual schemes respectively. Higher regularity of the schemes can be achieved by increasing the number of smoothing steps. These schemes can be nicely generalized to contain local shape parameters that allow the user to adjust locally the shape of the limit curve/surface.
      PubDate: 2017-03-13
      DOI: 10.1007/s10444-017-9519-y
  • A note on Taylor boundary conditions for accurate image restoration
    • Authors: Pietro Dell’Acqua
      Abstract: Abstract In recent years, several efforts were made in order to introduce boundary conditions for deblurring problems that allow to get accurate reconstructions. This resulted in the birth of Reflective, Anti-Reflective and Mean boundary conditions, which are all based on the idea of guaranteeing the continuity of the signal/image outside the boundary. Here we propose new boundary conditions that are obtained by suitably combining Taylor series and finite difference approximations. Moreover, we show that also Anti-Reflective and Mean boundary conditions can be attributed to the same framework. Numerical results show that, in case of low levels of noise and blurs able to perform a suitable smoothing effect on the original image (e.g. Gaussian blur), the proposed boundary conditions lead to a significant improvement of the restoration accuracy with respect to those available in the literature.
      PubDate: 2017-03-10
      DOI: 10.1007/s10444-017-9525-0
  • A fully diagonalized spectral method using generalized Laguerre functions
           on the half line
    • Authors: Fu-Jun Liu; Zhong-Qing Wang; Hui-Yuan Li
      Abstract: Abstract A fully diagonalized spectral method using generalized Laguerre functions is proposed and analyzed for solving elliptic equations on the half line. We first define the generalized Laguerre functions which are complete and mutually orthogonal with respect to an equivalent Sobolev inner product. Then the Fourier-like Sobolev orthogonal basis functions are constructed for the diagonalized Laguerre spectral method of elliptic equations. Besides, a unified orthogonal Laguerre projection is established for various elliptic equations. On the basis of this orthogonal Laguerre projection, we obtain optimal error estimates of the fully diagonalized Laguerre spectral method for both Dirichlet and Robin boundary value problems. Finally, numerical experiments, which are in agreement with the theoretical analysis, demonstrate the effectiveness and the spectral accuracy of our diagonalized method.
      PubDate: 2017-03-08
      DOI: 10.1007/s10444-017-9522-3
  • Solving F ( z + 1) = b F(z) in the complex plane
    • Authors: William Paulsen; Samuel Cowgill
      Abstract: Abstract The generalized tetration, defined by the equation F(z+1) = b F(z) in the complex plane with F(0) = 1, is considered for any b > e 1/e . By comparing other solutions to Kneser’s solution, natural conditions are found which force Kneser’s solution to be the unique solution to the equation. This answers a conjecture posed by Trappmann and Kouznetsov. Also, a new iteration method is developed which numerically approximates the function F(z) with an error of less than 10−50 for most bases b, using only 180 nodes, with each iteration gaining one or two places of accuracy. This method can be applied to other problems involving the Abel equation.
      PubDate: 2017-03-07
      DOI: 10.1007/s10444-017-9524-1
  • Improved maximum-norm a posteriori error estimates for linear and
           semilinear parabolic equations
    • Authors: Natalia Kopteva; Torsten Linß
      Abstract: Abstract Linear and semilinear second-order parabolic equations are considered. For these equations, we give a posteriori error estimates in the maximum norm that improve upon recent results in the literature. In particular it is shown that logarithmic dependence on the time step size can be eliminated. Semidiscrete and fully discrete versions of the backward Euler and of the Crank-Nicolson methods are considered. For their full discretizations, we use elliptic reconstructions that are, respectively, piecewise-constant and piecewise-linear in time. Certain bounds for the Green’s function of the parabolic operator are also employed.
      PubDate: 2017-03-02
      DOI: 10.1007/s10444-017-9514-3
  • Construction and analysis of higher order variational integrators for
           dynamical systems with holonomic constraints
    • Authors: Theresa Wenger; Sina Ober-Blöbaum; Sigrid Leyendecker
      Abstract: Abstract In this work, variational integrators of higher order for dynamical systems with holonomic constraints are constructed and analyzed. The construction is based on approximating the configuration and the Lagrange multiplier via different polynomials. The splitting of the augmented Lagrangian in two parts enables the use of different quadrature formulas to approximate the integral of each part. Conditions are derived that ensure the linear independence of the higher order constrained discrete Euler-Lagrange equations and stiff accuracy. Time reversibility is investigated for the discrete flow on configuration level only as for the flow on configuration and momentum level. The fulfillment of the hidden constraints plays an important role for the time reversibility of the presented integrators. The order of convergence is investigated numerically. Order reduction of the momentum and the Lagrange multiplier compared to the order of the configuration occurs in general, but can be avoided by fulfilling the hidden constraints in a simple post processing step. Regarding efficiency versus accuracy a numerical analysis yields that higher orders increase the accuracy of the discrete solution substantially while the computational costs decrease. A comparison to the constrained Galerkin methods in Marsden and West (Acta Numerica 10, 357–514 2001) and the symplectic SPARK integrators of Jay (SIAM Journal on Numerical Analysis 45(5), 1814–1842 2007) reveals that the approach presented here is more general and thus allows for more flexibility in the design of the integrator.
      PubDate: 2017-03-02
      DOI: 10.1007/s10444-017-9520-5
  • Second kind boundary integral equation for multi-subdomain diffusion
    • Authors: X. Claeys; R. Hiptmair; E. Spindler
      Abstract: Abstract We consider isotropic scalar diffusion boundary value problems whose diffusion coefficients are piecewise constant with respect to a partition of space into Lipschitz subdomains. We allow so-called material junctions where three or more subdomains may abut. We derive a boundary integral equation of the second kind posed on the skeleton of the subdomain partition that involves, as unknown, only one trace function at each point of each interface. We prove the well-posedness of the corresponding boundary integral equations. We also report numerical tests for Galerkin boundary element discretisations, in which the new approach proves to be highly competitive compared to the well-established first kind direct single-trace boundary integral formulation. In particular, GMRES seems to enjoy fast convergence independent of the mesh resolution for the discrete second kind BIE.
      PubDate: 2017-03-01
      DOI: 10.1007/s10444-017-9517-0
  • A study of the influence of center conditions on the domain of parameters
           of Newton’s method by using recurrence relations
    • Authors: J. A. Ezquerro; M. A. Hernández-Verón
      Abstract: Abstract This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.
      PubDate: 2017-02-28
      DOI: 10.1007/s10444-017-9518-z
  • A well-balanced van Leer-type numerical scheme for shallow water equations
           with variable topography
    • Authors: Dao Huy Cuong; Mai Duc Thanh
      Abstract: Abstract A well-balanced van Leer-type numerical scheme for the shallow water equations with variable topography is presented. The model involves a nonconservative term, which often makes standard schemes difficult to approximate solutions in certain regions. The construction of our scheme is based on exact solutions in computational form of local Riemann problems. Numerical tests are conducted, where comparisons between this van Leer-type scheme and a Godunov-type scheme are provided. Data for the tests are taken in both the subcritical region as well as supercritical region. Especially, tests for resonant cases where the exact solutions contain coinciding waves are also investigated. All numerical tests show that each of these two methods can give a good accuracy, while the van Leer -type scheme gives a better accuracy than the Godunov-type scheme. Furthermore, it is shown that the van Leer-type scheme is also well-balanced in the sense that it can capture exactly stationary contact discontinuity waves.
      PubDate: 2017-02-23
      DOI: 10.1007/s10444-017-9521-4
  • A family of non-oscillatory 6-point interpolatory subdivision schemes
    • Authors: Rosa Donat; Sergio López-Ureña; Maria Santágueda
      Abstract: Abstract In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered non-oscillatory versions of the 6-point Deslauries-Dubuc (DD) interpolatory scheme, just as the Power p schemes are considered nonlinear non-oscillatory versions of the 4-point DD interpolatory scheme. Their design principle may be related to that of the Power p schemes and it is based on a weighted analog of the Power p mean. We prove that the new schemes reproduce exactly polynomials of degree three and stay ’close’ to the 6-point DD scheme in smooth regions. In addition, we prove that the first and second difference schemes are well defined for each member of the family, which allows us to give a simple proof of the uniform convergence of these schemes and also to study their stability as in [19, 22]. However our theoretical study of stability is not conclusive and we perform a series of numerical experiments that seem to point out that only a few members of the new family of schemes are stable. On the other hand, extensive numerical testing reveals that, for smooth data, the approximation order and the regularity of the limit function may be similar to that of the 6-point DD scheme and larger than what is obtained with the Power p schemes.
      PubDate: 2017-02-14
      DOI: 10.1007/s10444-016-9509-5
  • Dimension-by-dimension moment-based central Hermite WENO schemes for
           directly solving Hamilton-Jacobi equations
    • Authors: Zhanjing Tao; Jianxian Qiu
      Abstract: Abstract In this paper, a class of high-order central Hermite WENO (HWENO) schemes based on finite volume framework and staggered meshes is proposed for directly solving one- and two-dimensional Hamilton-Jacobi (HJ) equations. The methods involve the Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. This work can be regarded as an extension of central HWENO schemes for hyperbolic conservation laws (Tao et al. J. Comput. Phys. 318, 222–251, 2016) which combine the central scheme and the HWENO spatial reconstructions and therefore carry many features of both schemes. Generally, it is not straightforward to design a finite volume scheme to directly solve HJ equations and a key ingredient for directly solving such equations is the reconstruction of numerical Hamiltonians to guarantee the stability of methods. Benefited from the central strategy, our methods require no numerical Hamiltonians. Meanwhile, the zeroth-order and the first-order moments of the solution are involved in the spatial HWENO reconstructions which is more compact compared with WENO schemes. The reconstructions are implemented through a dimension-by-dimension strategy when the spatial dimension is higher than one. A collection of one- and two- dimensional numerical examples is performed to validate high resolution and robustness of the methods in approximating the solutions of HJ equations, which involve linear, nonlinear, smooth, non-smooth, convex or non-convex Hamiltonians.
      PubDate: 2017-02-04
      DOI: 10.1007/s10444-017-9515-2
  • A fast discrete spectral method for stochastic partial differential
    • Authors: Yanzhao Cao; Ying Jiang; Yuesheng Xu
      Abstract: Abstract The goal of this paper is to construct an efficient numerical algorithm for computing the coefficient matrix and the right hand side of the linear system resulting from the spectral Galerkin approximation of a stochastic elliptic partial differential equation. We establish that the proposed algorithm achieves an exponential convergence with requiring only O \((n\log _{2}^{d+1}n)\) number of arithmetic operations, where n is the highest degree of the one dimensional orthogonal polynomial used in the algorithm, d+1 is the number of terms in the finite Karhunen–Loéve (K-L) expansion. Numerical experiments confirm the theoretical estimates of the proposed algorithm and demonstrate its computational efficiency.
      PubDate: 2017-02-04
      DOI: 10.1007/s10444-017-9513-4
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