Year: 2021
Author: Haili Qiao, Aijie Cheng
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 255–275
Abstract
The solutions of fractional equations with Caputo derivative often have a singularity at the initial time. Therefore, for numerical methods on uniform meshes it is difficult to achieve optimal convergence rates. To improve the convergence, Liu et al. [10] considered a finite difference method on non-uniform meshes. Following the ideas of [10], we introduce two more sets of non-uniform meshes and show that the corresponding discrete models have higher convergence rates. Besides, we apply the trapezoidal rule in the case of linear fractional partial differential equations. The results of numerical experiments are consistent with the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.190520.111020
East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 255–275
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Fractional differential equation weak singularity finite difference convergence analysis non-uniform meshes.