具有多变换参数的微分方程组两点边值问题

M. Filipchuk
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引用次数: 0

摘要

上午Samoilenko的数值解析方法是研究微分方程组各种边值问题解的可解性和近似构造的一种著名而有效的研究方法。用这种方法研究一类新的泛函微分方程组的边值问题仍然是一个实际问题。研究了线性两点边界条件下有限变换参数微分方程组的边值问题。为了研究这一问题的解的存在性和近似构造问题,我们使用了对A.M.Samoilenko的不确定方程的数值解析方法,即该方法只有一个解析分量。得到了所考虑的边值问题存在唯一解的充分条件和所构造的逐次逼近的误差估计。通过具体实例说明了改进后的方法的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ON A TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH MANY TRANSFORMED ARGUMENTS
A.M. Samoilenko’s numerical-analytic method is a well-known and effective research method of solvability and approximate construction of the solutions of various boundary value problems for systems of differential equations. The investigation of boundary value problems for new classes of systems of functional- differential equations by this method is still an actual problem. A boundary value problem for a system of differential equations with finite quantity of transformed arguments in the case of linear two-point boundary conditions is considered at this paper. In order to study the questions of the existence and approximate construction of a solution of this problem, we used a modification of A.M. Samoilenko’s numerical-analytic method without determining equation, i.e. the method has an analytical component only. Sufficient conditions for the existence of a unique solution of the considered boundary value problem and an error estimation of the constructed successive approximations are obtained. The use of the developed modification of the method is illustrated by concrete examples.
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