A Second-Order Difference Scheme for Generalized Time-Fractional Diffusion Equation with Smooth Solutions

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-05-23 DOI:10.1515/cmam-2022-0089

A. Khibiev, A. Alikhanov, Chengming Huang

引用次数: 4

Abstract

Abstract In the current work, we build a difference analog of the Caputo fractional derivative with generalized memory kernel (𝜇L2-1𝜎 formula). The fundamental features of this difference operator are studied, and on its ground, some difference schemes generating approximations of the second order in time for the generalized time-fractional diffusion equation with variable coefficients are worked out. We have proved stability and convergence of the given schemes in the grid L 2 L_{2} -norm with the rate equal to the order of the approximation error. The achieved results are supported by the numerical computations performed for some test problems.

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具有光滑解的广义时间分数阶扩散方程的二阶差分格式

摘要本文建立了具有广义记忆核的Caputo分数阶导数的差分模拟(𝜇L2-1公式)。研究了该差分算子的基本特征，并在此基础上给出了变系数广义时间分数扩散方程的二阶近似差分格式。在l2l_{2} -范数网格上证明了所给格式的稳定性和收敛性，其速率等于近似误差的阶数。通过对一些试验问题的数值计算，得到了较好的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.