One approach to solve a nonlinear boundary value problem for the Fredholm integro-differential equation

被引：4

作者：

Dzhumabaev, D. S. ^{[1
,2
]}

Mynbayeva, S. T. ^{[1
,3
]}

机构：

[1] Inst Math & Math Modeling, Alma Ata, Kazakhstan

[2] Int Informat Technol Univ, Alma Ata, Kazakhstan

[3] K Zhubanov Aktobe Reg State Univ, Aktobe, Kazakhstan

来源：

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2020年 / 97卷 / 01期

关键词：

quasilinear Fredholm integro-differential equation; quasilinear boundary value problem; a new general solution; iterative process; ALGORITHM;

D O I：

10.31489/2020M1/27-36

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A quasilinear boundary value problem for a Fredholm integro-differential equation is considered. The interval is divided into N parts and the values of the solution to the equation at the left end points of the subintervals are introduced as additional parameters. New unknown functions are introduced on the subintervals and a special Cauchy problem with parameters is solved with respect to a system of such functions. By means of the solution to this problem, a new general solution to the quasilinear Fredholm integro-differential equation is constructed. The conditions of the existence of a unique new general solution to the equation under consideration are obtained. A new general solution is used to create a system of nonlinear algebraic equations in parameters introduced. The conditions for the existence of a unique solution to this system are established. This ensures the existence of a unique solution to original problem

引用

页码：27 / 36

页数：10

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