Численное решение интегральных уравнений Вольтерра I рода с кусочно-непрерывными ядрами

D. N. Sidorov; A. N. Tynda; I. R. Muftahov

Authors

D. N. Sidorov Irkutsk State Technical University, Irkutsk State University, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences
A. N. Tynda Penza State University
I. R. Muftahov Irkutsk State Technical University

Keywords:

Volterra integral equations of the 1st kind, evolving systems, Glushkov integral model, numerical method

Abstract

Integral equations are in the core of many mathematical models in physics, economics and ecology. Volterra integral equations of the first kind with jump discontinuous kernels play important role in such models and they are considered in this article. Regularization method and sufficient conditions for existence and uniqueness of the solution of such integral equations are derived. An efficient numerical method based on the mid-rectangular quadrature rule for these equations with jump discontinuous kernels is proposed. The accuracy of proposed numerical method is O(N −1 ). The model examples demonstrate efficiency of proposed method: errors, two mesh differences and orders of convergent

Author Biographies

D. N. Sidorov, Irkutsk State Technical University, Irkutsk State University, Energy Systems Institute, Siberian Branch of Russian Academy of Sciences

кандидат физико-математических наук, доцент кафедры≪Вычислительная техника≫

A. N. Tynda, Penza State University

кандидат физико-математических наук, доцент кафедры≪Высшая и прикладная математика≫

I. R. Muftahov, Irkutsk State Technical University

аспирант кафедры ≪Вычислительная техника≫

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