一维和二维时间分形扩散方程的 Sinc-Galerkin 方法和高阶方法

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-09-06 DOI:10.1186/s13661-024-01915-6

Man Luo, Da Xu, Xianmin Pan

{"title":"一维和二维时间分形扩散方程的 Sinc-Galerkin 方法和高阶方法","authors":"Man Luo, Da Xu, Xianmin Pan","doi":"10.1186/s13661-024-01915-6","DOIUrl":null,"url":null,"abstract":"In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"27 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations\",\"authors\":\"Man Luo, Da Xu, Xianmin Pan\",\"doi\":\"10.1186/s13661-024-01915-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.\",\"PeriodicalId\":49228,\"journal\":{\"name\":\"Boundary Value Problems\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boundary Value Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13661-024-01915-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01915-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文提出了一种求解一维（1D）和二维（2D）时间分数扩散方程的新数值算法。空间离散化采用 Sinc-Galerkin 方案，时间离散化采用高阶有限差分公式。本文分析了这些方法的收敛行为，并给出了误差边界。本文的主要目的是利用 Sinc-Galerkin 方法提出二维问题的误差边界。本文利用 Sinc 函数的特性详细研究了所提出方法的收敛性，并提出了二维问题的最佳指数收敛率。一些数值实验验证了理论结果，并展示了所提方案的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations

In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.