A spatial sixth-order numerical scheme for solving fractional partial differential equation

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-08-14 DOI:10.1016/j.aml.2024.109265

引用次数: 0

Abstract

In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is $O (τ^{2} + h^{6})$ , where $τ$ and $h$ are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.

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求解分数偏微分方程的空间六阶数值方案

本文提出了一种求解时间分数扩散方程（TFDE）的空间六阶数值方案。所建数值方案的收敛阶数为 O(τ2+h6)，其中 τ 和 h 分别为时间步长和空间步长。利用傅立叶方法给出了拟议方案的稳定性和误差估计。研究了一些数值示例，以证明该方案的正确性和有效性，并验证理论分析。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.

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