Direct regularization for system of integral-algebraic equations of index-1

It is known that the coupled system consisting of Volterra integral equations of the first and second kind belongs to the class of moderately ill-posed problems. In the present paper, we are interested in numerical solution of Volterra integral-algebraic equations by a direct regularization method,...

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Bibliographic Details
Published inInverse problems in science and engineering Vol. 26; no. 5; pp. 728 - 743
Main Authors Farahani, M. S., Hadizadeh, M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 04.05.2018
Subjects
Ill-posed problem
Lavrentiev's iterated method
numerical treatments
regularization parameter
Volterra integral-algebraic equations
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Summary:It is known that the coupled system consisting of Volterra integral equations of the first and second kind belongs to the class of moderately ill-posed problems. In the present paper, we are interested in numerical solution of Volterra integral-algebraic equations by a direct regularization method, i.e. an approach which does not make use of the adjoint operator as well as any reduction or remodelling of the original problem. A numerical algorithm based on Lavrentiev's regularization iterated method is constructed that preserves the Volterra structure of the original problem. The convergence analysis of the proposed method is given and its validity and efficiency are also demonstrated through several numerical experiments.
ISSN:1741-5977
1741-5985
DOI:10.1080/17415977.2017.1347169