Finite difference approximation of space-fractional diffusion problems: the matrix transformation method

DOI10.1016/j.camwa.2016.11.021zbMath1368.65148OpenAlexW2563784679MaRDI QIDQ2013809

Ferenc Izsák, Béla J. Szekeres

Publication date: 9 August 2017

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.11.021

zbMATH Keywords

finite difference methodmatrix transformation methodfractional-order diffusion

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Related Items (9)

Models of space-fractional diffusion: a critical review ⋮ Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model ⋮ Finite element methods for fractional-order diffusion problems with optimal convergence order ⋮ Efficient computation of matrix power-vector products: application for space-fractional diffusion problems ⋮ Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix ⋮ A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems ⋮ Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator ⋮ Optimal approximation of internal controls for a wave-type problem with fractional Laplacian using finite-difference method ⋮ Computing the matrix fractional power with the double exponential formula

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast finite volume methods for space-fractional diffusion equations
• Fractional elliptic equations, Caccioppoli estimates and regularity
• The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
• Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations
• A second order finite difference-spectral method for space fractional diffusion equations
• Finite element approximation of fractional order elliptic boundary value problems
• A second-order accurate numerical method for the two-dimensional fractional diffusion equation
• Heat kernel estimates for the Dirichlet fractional Laplacian
• A lower bound for the smallest singular value of a matrix
• Finite difference approximations for fractional advection-dispersion flow equations
• Sharp estimates for Dirichlet eigenfunctions in simply connected domains
• Quasi-compact finite difference schemes for space fractional diffusion equations
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Geometrical Structure of Laplacian Eigenfunctions
• A restarted Lanczos approximation to functions of a symmetric matrix
• $hp$-Finite Elements for Elliptic Eigenvalue Problems: Error Estimates Which Are Explicit with Respect to $\lambda$, h, and p
• A Schur–Padé Algorithm for Fractional Powers of a Matrix
• A series of high-order quasi-compact schemes for space fractional diffusion equations based on the superconvergent approximations for fractional derivatives
• A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations
• A class of second order difference approximations for solving space fractional diffusion equations
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations

This page was built for publication: Finite difference approximation of space-fractional diffusion problems: the matrix transformation method