一类非线性Fredholm积分微分方程边值问题的可解性

IF 0.7 Q2 MATHEMATICS
A. Assanova, S. Zhumatov, S. Mynbayeva, S. Karakenova
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引用次数: 0

摘要

本文提出了一种求解Fredholm积分微分方程非线性边值问题的构造方法。利用D.S.Dzhumabaev参数化方法,将所考虑的问题转化为子区间上有参数的非线性积分微分方程组的等效边值问题。将参数化方法应用于非线性Fredholm积分微分方程时,中间问题是一个具有参数的非线性积分微分方程组的特殊Cauchy问题。通过将带参数的特殊Cauchy问题的解代入边界条件和原问题解在内部划分点的连续性条件,我们构造了一个带参数的非线性代数方程组。证明了该系统的可解性提供了原边值问题解的存在性。迭代方法用于求解构造的参数代数方程组和特殊的Cauchy问题。给出了一种求解所考虑的边值问题的算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On solvability of boundary value problem for a nonlinear Fredholm integro-differential equation
The paper proposes a constructive method to solve a nonlinear boundary value problem for a Fredholm integro-differential equation. Using D.S. Dzhumabaev parametrization method, the problem under consideration is transformed into an equivalent boundary value problem for a system of nonlinear integrodifferential equations with parameters on the subintervals. When applying the parametrization method to a nonlinear Fredholm integro-differential equation, the intermediate problem is a special Cauchy problem for a system of nonlinear integro-differential equations with parameters. By substitution the solution to the special Cauchy problem with parameters into the boundary condition and the continuity conditions of the solution to the original problem at the interior partition points, we construct a system of nonlinear algebraic equations in parameters. It is proved that the solvability of this system provides the existence of a solution to the original boundary value problem. The iterative methods are used to solve both the constructed system of algebraic equations in parameters and the special Cauchy problem. An algorithm for solving boundary value problem under consideration is provided.
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来源期刊
CiteScore
1.20
自引率
50.00%
发文量
50
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