Two Regularization Methods for Identifying the Initial Value of Time-Fractional Telegraph Equation

In this article, an inverse problem for identifying the initial value of time-fractional telegraph equation is addressed. This is a typical ill-posed problem, meaning the solution does not depend continuously on the data. Besides, we give the conditional stability result based on an a priori bound c...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics
Main Authors Liang, Ying-Qing, Yang, Fan, Li, Xiao-Xiao
Format Journal Article
LanguageEnglish
Published 15.01.2025
Online AccessGet full text
ISSN1609-4840
1609-9389
DOI10.1515/cmam-2024-0159

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Summary:In this article, an inverse problem for identifying the initial value of time-fractional telegraph equation is addressed. This is a typical ill-posed problem, meaning the solution does not depend continuously on the data. Besides, we give the conditional stability result based on an a priori bound condition. We utilize the modified quasi-boundary regularization method and the Landweber iterative regularization method to obtain the corresponding approximate solutions, respectively. The convergent error estimates under the a priori regularization parameter selection rule and the a posteriori regularization parameter selection rule are given. Some numerical experiments testify the effectiveness and precision of the proposed methods.
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2024-0159