Identification of an Inverse Source Problem in a Fractional Partial Differential Equation Based on Sinc-Galerkin Method and TSVD Regularization

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-06-06 DOI:10.1515/cmam-2022-0178

A. Safaie, A. H. Salehi Shayegan, M. Shahriari

引用次数: 0

Abstract

Abstract In this paper, using Sinc-Galerkin method and TSVD regularization, an approximation of the quasi-solution to an inverse source problem is obtained. To do so, the solution of direct problem is obtained by the Sinc-Galerkin method, and this solution is applied in a least squares cost functional. Then, to obtain an approximation of the quasi-solution, we minimize the cost functional by TSVD regularization. Error analysis and convergence of the proposed method are investigated. In addition, at the end, four numerical examples are given in details to show the efficiency and accuracy of the proposed method.

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基于c-伽辽金方法和TSVD正则化的分数阶偏微分方程逆源问题辨识

摘要本文利用Sinc-Galerkin方法和TSVD正则化，得到了一个反源问题拟解的近似解。为此，通过Sinc-Galerkin方法获得了直接问题的解，并将该解应用于最小二乘成本函数中。然后，为了获得拟解的近似，我们通过TSVD正则化最小化成本函数。研究了该方法的误差分析和收敛性。最后，通过四个算例详细说明了该方法的有效性和准确性。

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.