SOLVABILITY AND NUMERICAL SOLUTIONS OF SYSTEMS OF NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND WITH PIECEWISE CONTINUOUS KERNELS

被引：8

作者：

Muftahov, I. R. ^{[1
]}

Sidorov, D. N. ^{[1
,2
,3
]}

机构：

[1] Irkutsk Natl Res Tech Univ, Irkutsk, Russia

[2] Russian Acad Sci, Melentiev Energy Syst Inst, Siberian Branch, Irkutsk 664003, Russia

[3] Irkutsk State Univ, Irkutsk 664003, Russia

来源：

BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE | 2016年 / 9卷 / 01期

关键词：

Volterra integral equations; discontinuous kernel; ill-posed problem; evolving dynamical systems; quadrature; Dekker - Brent method;

D O I：

10.14529/mmp160111

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence theorem for systems of nonlinear Volterra integral equations kernels of the first kind with piecewise continuous is proved. Such equations model evolving dynamical systems. A numerical method for solving nonlinear Volterra integral equations of the first kind with piecewise continuous kernels is proposed using midpoint quadrature rule. Also numerical method for solution of systems of linear Volterra equations of the first kind is described. The examples demonstrate efficiency of proposed algorithms. The accuracy of proposed numerical methods is o(N-1).

引用

页码：130 / 136

页数：7

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