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  Subjects -> MATHEMATICS (Total: 968 journals)
    - APPLIED MATHEMATICS (84 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (22 journals)
    - PROBABILITIES AND MATH STATISTICS (85 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 28)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
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: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 5)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
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: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
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: 5)
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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
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)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
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: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
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: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 12)
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: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
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)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
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: 1)
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: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
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: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 5)
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: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
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: 29)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)

        1 2 3 4 | Last

Journal Cover BIT Numerical Mathematics
  [SJR: 1.221]   [H-I: 40]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1572-9125 - ISSN (Online) 0006-3835
   Published by Springer-Verlag Homepage  [2350 journals]
  • A posteriori error estimates for the one and one-half Dimensional
           Relativistic Vlasov–Maxwell system
    • Authors: Mohammad Asadzadeh; Christoffer Standar
      Pages: 5 - 26
      Abstract: This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov–Maxwell system. The SD scheme yields a weak formulation, that corresponds to an add of extra diffusion to, e.g. the system of equations having hyperbolic nature, or convection-dominated convection diffusion problems. The a posteriori error estimates rely on dual formulations and yield error controls based on the computable residuals. The convergence estimates are derived in negative norms, where the error is split into an iteration and an approximation error and the iteration procedure is assumed to converge.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0666-9
      Issue No: Vol. 58, No. 1 (2018)
       
  • Evaluation schemes in the ring of quaternionic polynomials
    • Authors: M. Irene Falcão; Fernando Miranda; Ricardo Severino; M. Joana Soares
      Pages: 51 - 72
      Abstract: In this paper we focus on computational aspects associated with polynomial problems in the ring of one-sided quaternionic polynomials. The complexity and error bounds of quaternion arithmetic are considered and several evaluation schemes are analyzed from their complexity point of view. The numerical stability of generalized Horner’s and Goertzel’s algorithms to evaluate polynomials with quaternion floating-point coefficients is addressed. Numerical tests illustrate the behavior of the algorithms from the point of view of performance and accuracy.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0667-8
      Issue No: Vol. 58, No. 1 (2018)
       
  • A splitting method for the augmented Burgers equation
    • Authors: Liviu I. Ignat; Alejandro Pozo
      Pages: 73 - 102
      Abstract: In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic expansion. We prove that, when time increases, these solutions behave as the self-similar solutions of the viscous Burgers equation.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0673-x
      Issue No: Vol. 58, No. 1 (2018)
       
  • Adaptive semi-discrete formulation of BSQI–WENO scheme for the modified
           Burgers’ equation
    • Authors: Rakesh Kumar
      Pages: 103 - 132
      Abstract: In this article, we have proposed a septic B-spline quasi-interpolation (SeBSQI) based numerical scheme for the modified Burgers’ equation. The SeBSQI scheme maintains eighth order accuracy for the smooth solution, but fails to maintain a non-oscillatory profile when the solution has discontinuities or sharp variations. To ensure the non-oscillatory profile of the solution, we have proposed an adaptive SeBSQI (ASeBSQI) scheme for the modified Burgers’ equation. The ASeBSQI scheme maintains higher order accuracy in the smooth regions using SeBSQI approximation and in regions with discontinuities or sharp variations, 5th order weighted essentially non-oscillatory (WENO) reconstruction is used to preserve a non-oscillatory profile. To identify discontinuous or sharp variation regions, a weak local truncation error based smooth indicator is proposed for the modified Burgers’ equation. For the temporal derivative, we have considered the Runge–Kutta method of order four. We have shown numerically that the ASeBSQI scheme preserves the convergence rate of the SeBSQI and it converges to the exact solution with convergence rate eight. We have performed numerical experiments to validate the proposed scheme. The numerical experiments demonstrate an improvement in accuracy and efficiency of the proposed schemes over the WENO5 and septic B-spline collocation schemes. The ASeBSQI scheme is also tested for one-dimensional Euler equations.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0675-8
      Issue No: Vol. 58, No. 1 (2018)
       
  • On restarting the tensor infinite Arnoldi method
    • Authors: Giampaolo Mele; Elias Jarlebring
      Pages: 133 - 162
      Abstract: An efficient and robust restart strategy is important for any Krylov-based method for eigenvalue problems. The tensor infinite Arnoldi method (TIAR) is a Krylov-based method for solving nonlinear eigenvalue problems (NEPs). This method can be interpreted as an Arnoldi method applied to a linear and infinite dimensional eigenvalue problem where the Krylov basis consists of polynomials. We propose new restart techniques for TIAR and analyze efficiency and robustness. More precisely, we consider an extension of TIAR which corresponds to generating the Krylov space using not only polynomials, but also structured functions, which are sums of exponentials and polynomials, while maintaining a memory efficient tensor representation. We propose two restarting strategies, both derived from the specific structure of the infinite dimensional Arnoldi factorization. One restarting strategy, which we call semi-explicit TIAR restart, provides the possibility to carry out locking in a compact way. The other strategy, which we call implicit TIAR restart, is based on the Krylov–Schur restart method for the linear eigenvalue problem and preserves its robustness. Both restarting strategies involve approximations of the tensor structured factorization in order to reduce the complexity and the required memory resources. We bound the error introduced by some of the approximations in the infinite dimensional Arnoldi factorization showing that those approximations do not substantially influence the robustness of the restart approach. We illustrate the effectiveness of the approaches by applying them to solve large scale NEPs that arise from a delay differential equation and a wave propagation problem. The advantages in comparison to other restart methods are also illustrated.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0671-z
      Issue No: Vol. 58, No. 1 (2018)
       
  • Explicit pseudo-symplectic methods for stochastic Hamiltonian systems
    • Authors: Xinyan Niu; Jianbo Cui; Jialin Hong; Zhihui Liu
      Pages: 163 - 178
      Abstract: We construct stochastic pseudo-symplectic methods and analyze their pseudo-symplectic orders for stochastic Hamiltonian systems with additive noises in this paper. All of these methods are explicit so that the numerical implementations become much easier than implicit methods. Through the numerical experiments, we find that these methods have desired properties in accuracy and stability as well as the preservation of the symplectic structure of the systems.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0668-7
      Issue No: Vol. 58, No. 1 (2018)
       
  • Anti-Gaussian quadrature formulae based on the zeros of Stieltjes
           polynomials
    • Authors: Sotirios E. Notaris
      Pages: 179 - 198
      Abstract: It is well known that the Gauss–Kronrod quadrature formula does not always exist with real and distinct nodes and positive weights. In 1996, in an attempt to find an alternative to the Gauss–Kronrod formula for estimating the error of the Gauss quadrature formula, Laurie constructed the anti-Gaussian quadrature formula, which always has real and distinct nodes and positive weights. First, we give a description and prove the most important properties of the anti-Gaussian formula, by applying a different approach than that of Laurie. Then, we consider a measure such that the respective (monic) orthogonal polynomials, above a specific index, satisfy a three-term recurrence relation with constant coefficients. We show that for a measure of this kind the nodes of the anti-Gaussian formula are the zeros of the respective Stieltjes polynomial, while the resulting averaged Gaussian quadrature formula is precisely the corresponding Gauss–Kronrod formula, having elevated degree of exactness. Moreover, we show, by a new method, that a symmetric Gauss–Lobatto quadrature formula is a modified anti-Gaussian formula, and we specialize our results to the measures with constant recurrence coefficients.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0672-y
      Issue No: Vol. 58, No. 1 (2018)
       
  • Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods
           for systems of initial value problems
    • Authors: Tomoaki Okayama
      Pages: 199 - 220
      Abstract: A Sinc-collocation method was proposed by Stenger, who also gave a theoretical analysis of the method in the case of a “scalar” equation. This paper extends the theoretical results to the case of a “system” of equations. Furthermore, this paper proposes a more efficient method by replacing the variable transformation employed in Stenger’s method. The efficiency was confirmed by both a theoretical analysis and some numerical experiments. In addition to the existing and newly proposed Sinc-collocation methods, this paper also gives similar theoretical results for the Sinc-Nyström methods proposed by Nurmuhammad et al. In terms of computational cost, the newly proposed Sinc-collocation method is the most efficient among these methods.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0663-z
      Issue No: Vol. 58, No. 1 (2018)
       
  • Pointwise estimates of SDFEM on Shishkin triangular meshes for problems
           with exponential layers
    • Authors: Jin Zhang; Xiaowei Liu
      Pages: 221 - 246
      Abstract: In this paper, we present a pointwise convergence analysis for a streamline diffusion finite element method (SDFEM) on a Shishkin triangular mesh. We prove that the method is uniformly convergent with a pointwise accuracy of order almost 7/4 (up to a logarithmic factor) away from the subdomain where the layers intersect. Finally, numerical experiments support our theoretical results.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0661-1
      Issue No: Vol. 58, No. 1 (2018)
       
  • Correction to: Multilevel Monte Carlo front-tracking for random scalar
           conservation laws
    • Authors: Nils Henrik Risebro; Christoph Schwab; Franziska Weber
      Pages: 247 - 255
      Abstract: An error in [4, Theorem 4.1, 4.5, Corollary 4.5] is corrected. There, in the Monte Carlo error bounds for front tracking for scalar conservation laws with random input data, 2-integrability in a Banach space of type 1 was assumed. In providing the corrected convergence rate bounds and error versus work analysis of multilevel Monte Carlo front-tracking methods, we also generalize [4] to q-integrability of the random entropy solution for some \(1<q\le 2\) , allowing possibly infinite variance of the random entropy solutions of the scalar conservation law.
      PubDate: 2018-03-01
      DOI: 10.1007/s10543-017-0670-0
      Issue No: Vol. 58, No. 1 (2018)
       
  • A Lyapunov and Sacker–Sell spectral stability theory for one-step
           methods
    • Authors: Andrew J. Steyer; Erik S. Van Vleck
      Abstract: Approximation theory for Lyapunov and Sacker–Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent (nonautonomous) linear ordinary differential equation (ODE) initial value problem in terms of the local error. Integral separation is used to characterize the conditioning of stability spectra calculations. The stability of the numerical solution by a one-step method of a nonautonomous linear ODE using real-valued, scalar, nonautonomous linear test equations is justified. This analysis is used to approximate exponential growth/decay rates on finite and infinite time intervals and establish global error bounds for one-step methods approximating uniformly, exponentially stable trajectories of nonautonomous and nonlinear ODEs. A time-dependent stiffness indicator and a one-step method that switches between explicit and implicit Runge–Kutta methods based upon time-dependent stiffness are developed based upon the theoretical results.
      PubDate: 2018-04-13
      DOI: 10.1007/s10543-018-0704-2
       
  • Solution methods for linear discrete ill-posed problems for color image
           restoration
    • Authors: A. H. Bentbib; M. El Guide; K. Jbilou; E. Onunwor; L. Reichel
      Abstract: This work discusses four algorithms for the solution of linear discrete ill-posed problems with several right-hand side vectors. These algorithms can be applied, for instance, to multi-channel image restoration when the image degradation model is described by a linear system of equations with multiple right-hand sides that are contaminated by errors. Two of the algorithms are block generalizations of the standard Golub–Kahan bidiagonalization method with the block size equal to the number of channels. One algorithm uses standard Golub–Kahan bidiagonalization without restarts for all right-hand sides. These schemes are compared to standard Golub–Kahan bidiagonalization applied to each right-hand side independently. Tikhonov regularization is used to avoid severe error propagation. Numerical examples illustrate the performance of these algorithms. Applications include the restoration of color images.
      PubDate: 2018-04-12
      DOI: 10.1007/s10543-018-0706-0
       
  • Unconditionally positive and conservative third order modified
           Patankar–Runge–Kutta discretizations of production–destruction
           systems
    • Authors: Stefan Kopecz; Andreas Meister
      Abstract: Modified Patankar–Runge–Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production–destruction systems. They adapt explicit Runge–Kutta schemes to ensure positivity and conservation irrespective of the time step size. The first two members of this class, the first order MPE scheme and the second order MPRK22(1) scheme, have been successfully applied in a large number of applications. Recently, a general definition of MPRK schemes was introduced and necessary as well as sufficient conditions to obtain first and second order MPRK schemes were presented. In this paper we derive necessary and sufficient conditions for third order MPRK schemes and introduce the first family of such schemes. The theoretical results are confirmed by numerical experiments considering linear and nonlinear as well as nonstiff and stiff systems of differential equations.
      PubDate: 2018-03-27
      DOI: 10.1007/s10543-018-0705-1
       
  • Numerical integration using integrals over hyperplane sections of
           simplices in a triangulation of a polytope
    • Authors: Allal Guessab; Boris Semisalov
      Abstract: In this paper, we consider the problem of approximating a definite integral of a given function f when, rather than its values at some points, a number of integrals of f over some hyperplane sections of simplices in a triangulation of a polytope P in \(\mathbb {R}^d\) are only available. We present several new families of “extended” integration formulas, all of which are a weighted sum of integrals over some hyperplane sections of simplices, and which contain in a special case of our result multivariate analogues of the midpoint rule, the trapezoidal rule and the Simpson’s rule. Along with an efficient algorithm for their implementations, several illustrative numerical examples are provided comparing these cubature formulas among themselves. The paper also presents the best possible explicit constants for their approximation errors. We perform numerical tests which allow the comparison of the new cubature formulas. Finally, we will discuss a conjecture suggested by the numerical results.
      PubDate: 2018-03-24
      DOI: 10.1007/s10543-018-0703-3
       
  • A parallel spectral deferred correction method for first-order evolution
           problems
    • Authors: Shuai Zhu; Shilie Weng
      Abstract: This paper investigates a novel parallel technique based on the spectral deferred correction (SDC) method and a compensation step for solving first-order evolution problems, and we call it para-SDC method for convenience. The standard SDC method is used in parallel with a rough initial guess and a Picard integral equation with high precision initial condition is acted as a compensator. The goal of this paper is to show how these processes can be parallelized and how to improve the efficiency. During the SDC step an implicit or semi-implicit method can be used for stiff problems which is always time-consuming, therefore that’s why we do this procedure in parallel. Due to a better initial condition of parallel intervals after the SDC step, the goal of compensation step is to get a better approximation and also avoid of solving an implicit problem again. During the compensation step an explicit Picard scheme is taken based on the numerical integration with polynomial interpolation on Gauss Radau II nodes, which is almost no time consumption, obviously, that’s why we do this procedure in serial. The convergency analysis and the parallel efficiency of our method are also discussed. Several numerical experiments and an application for simulation Allen–Cahn equation are presented to show the accuracy, stability, convergence order and efficiency features of para-SDC method.
      PubDate: 2018-03-14
      DOI: 10.1007/s10543-018-0702-4
       
  • Relative perturbation bounds for eigenpairs of diagonalizable matrices
    • Authors: Yanmei Chen; Xiaofei Peng; Wen Li
      Abstract: In this paper, we present some uniform relative perturbation bounds for eigenvalues and eigenspaces of diagonalizable matrices under additive and multiplicative perturbations. Some existing perturbation bounds can be improved based on the new bounds. Numerical experiments are given to demonstrate the advantage of the new bounds.
      PubDate: 2018-03-08
      DOI: 10.1007/s10543-018-0701-5
       
  • Efficient preconditioner of one-sided space fractional diffusion equation
    • Authors: Xue-Lei Lin; Michael K. Ng; Hai-Wei Sun
      Abstract: In this paper, we propose an efficient preconditioner for the linear systems arising from the one-sided space fractional diffusion equation with variable coefficients. The shifted Gr \(\ddot{\mathrm{u}}\) nwald formula is employed to discretize the one-sided Riemann–Liouville fractional derivative. The matrix structure of resulting linear systems is Toeplitz-like, which is a summation of an identity matrix and a diagonal-times-nonsymmetric-Toeplitz matrix. A diagonal-times-nonsymmetric-Toeplitz preconditioner is proposed to reduce the condition number of the Toeplitz-like matrix, where the diagonal part comes from the variable coefficients and the nonsymmetric Toeplitz part comes from the Riemann–Liouville derivative. Theoretically, we show that the condition number of the preconditioned matrix is uniformly bounded by a constant independent of discretization step-sizes under certain assumptions on the coefficient function. Due to the uniformly bounded condition number, the Krylov subspace method for the preconditioned linear systems converges linearly and independently on discretization step-sizes. Numerical results are reported to show the efficiency of the proposed preconditioner and to demonstrate its superiority over other tested preconditioners.
      PubDate: 2018-02-27
      DOI: 10.1007/s10543-018-0699-8
       
  • An efficient fourth-order in space difference scheme for the nonlinear
           fractional Ginzburg–Landau equation
    • Authors: Pengde Wang; Chengming Huang
      Abstract: This paper proposes and analyzes a high-order implicit-explicit difference scheme for the nonlinear complex fractional Ginzburg–Landau equation involving the Riesz fractional derivative. For the time discretization, the second-order backward differentiation formula combined with the explicit second-order Gear’s extrapolation is adopted. While for the space discretization, a fourth-order fractional quasi-compact method is used to approximate the Riesz fractional derivative. The scheme is efficient in the sense that, at each time step, only a linear system with a coefficient matrix independent of the time level needs to be solved. Despite of the explicit treatment of the nonlinear term, the scheme is shown to be unconditionally convergent in the \(l^2_h\) norm, semi- \(H^{\alpha /2}_h\) norm and \(l^\infty _h\) norm at the order of \(O(\tau ^2+h^4)\) with \(\tau \) time step and h mesh size. Numerical tests are provided to confirm the accuracy and efficiency of the scheme.
      PubDate: 2018-02-14
      DOI: 10.1007/s10543-018-0698-9
       
  • Multivariate polynomial interpolation using even and odd polynomials
    • Authors: J. M. Carnicer; C. Godés
      Abstract: The Lebesgue constant is a measure for the stability of the Lagrange interpolation. The decomposition of the Lagrange interpolation operator in their even and odd parts with respect to the last variable can be used to find a relation between the Lebesgue constant for a space of polynomials and the corresponding Lebesgue constants for subspaces of even and odd polynomials. It is shown that such a decomposition preserves the stability properties of the Lagrange interpolation operator. We use the Lebesgue functions to provide pointwise quantitative measures of the stability properties and illustrate with examples the behaviour in simple cases.
      PubDate: 2017-12-01
      DOI: 10.1007/s10543-017-0674-9
       
 
 
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