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Numerical Solution of Integral-Algebraic Equations with a Weak Boundary Singularity by k-step Methods

Авторы: Botoroeva M.N., Budnikova O.S., Bulatov M.V., Orlov S.S.

Журнал: Journal Computational Mathematics and Mathematical Physics

Том: 61

Номер: 11

Год: 2021

Отчётный год: 2021

Издательство:

Местоположение издательства:

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Проекты:

DOI: 10.1134/⁠S096554252111004X

Аннотация: The article presents the construction of k-step methods for solving systems of Volterra integral equations of the first and the second kind with a weak power-law singularity of the kernels in the lower limit of integration. The matrix-vector representation of such systems has the form of an abstract equation with a degenerate coefficient matrix at the nonintegral terms, which is called an integral-algebraic equation. The methods proposed are based on extrapolation formulas for the principal part, Adams-type multistep methods, and a product integration formula for the integral term. The weights of the quadrature formulas constructed are obtained explicitly. A theorem on the convergence of the methods developed is proved. The theoretical results are illustrated by numerical calculations of test examples.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Да

Индексируется ВАК: Нет

Индексируется CORE: Нет

Публикация в печати: 0