Journal
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
Volume 26, Issue 5, Pages 728-743Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17415977.2017.1347169
Keywords
Ill-posed problem; Lavrentiev's iterated method; regularization parameter; Volterra integral-algebraic equations; numerical treatments
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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.
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