High Order Finite Difference Methods on Non-uniform Meshes for Space Fractional Operators

Abstract

In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform meshes. The nonlocal property of space fractional operator makes it difficult to design the finite difference scheme on non-uniform meshes. This paper provides a basic strategy to derive the first and high order discretization schemes on non-uniform meshes for fractional operators. And the obtained first and second schemes on non-uniform meshes are used to solve space fractional diffusion equations. The error estimates and stability analysis are detailedly performed; and extensive numerical experiments confirm the theoretical analysis or verify the convergence orders.

42 pages, 8 figures

References in corpus (3)

• High order algorithms for the fractional substantial diffusion equation with truncated Lévy flights
• A Series of High Order Quasi-Compact Schemes for Space Fractional Diffusion Equations Based on the Superconvergent Approximations for Fractional Derivatives
• Second order WSGD operators II: A new family of difference schemes for space fractional advection diffusion equation

Cited by in corpus (2)

• A preconditioning technique for all-at-once system from the nonlinear tempered fractional diffusion equation
• On spectral Petrov-Galerkin method for solving fractional initial value problems in weighted Sobolev space