New General Solution to a Quasilinear Fredholm Integro-Differential Equation and Its Application

被引：1
|
作者：
Assanova, A. T. [1 ]
Mynbayeva, S. T. [1 ,2 ]
机构：
[1] Inst Math & Math Modeling, Alma Ata, Kazakhstan
[2] Zhubanov Aktobe Reg Univ, Aktobe, Kazakhstan
来源：
LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 10期
关键词：
quasilinear Fredholm integro-differential equation; new general solution; two-point boundary value problem; parametrization method; solvability conditions; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; SOLVABILITY; ALGORITHM; SOLVE;
D O I：
10.1134/S1995080223100062
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A quasilinear Fredholm integro-differential equation is considered on a finite interval. By using Dzhumabaev parametrization method the integro-differential equation is reduced to a special Cauchy problem. The sufficient conditions of the existence of a unique solution to the special Cauchy problem are established, and a new general solution to the integro-differential equation is constructed using this solution. The new general solution is used to solve a boundary value problem, the conditions for the existence of a unique solution to the boundary value problem are obtained.
引用
收藏
页码：4231 / 4239
页数：9
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