Backward difference formulae and spectral Galerkin methods for the Riesz space fractional diffusion equation

Yang Xu, Yanming Zhang and Jingjun Zhao

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 166, issue C, 494-507

Abstract: Approximating Riesz space fractional diffusion equation in time by k-step backward difference formula and in space by spectral Galerkin method, we establish a fully discrete scheme with high order both in time and in space. For k≤5, we prove the stability of full discretization and obtain the error estimate with order O(τk+Nα2−m), which depends only on the regularity of initial value and right-hand function. Moreover, we extend the proposed method to two dimensional case and derive similar results. Finally, we illustrate the theoretical estimates by numerical examples.

Keywords: Backward difference formula; Spectral Galerkin method; Riesz space fractional diffusion equation; Stability; Convergence (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:166:y:2019:i:c:p:494-507

DOI: 10.1016/j.matcom.2019.07.007

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