A computational method for solving a boundary value problem for impulsive integro-differential equation

IF 0.2 Q4 MATHEMATICS
A. K. Tankeyeva, S. Mynbayeva
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引用次数: 0

Abstract

. In this paper, we are interested in finding a numerical solution of a linear BVP for a Fredholm IDE with a degenerate kernel subjected to impulsive actions. By Dzumabaev’s parametrization method the original problem is reduced to a multipoint BVP for the system of Fredholm IDEs with additional parameters. For fixed parameters, the special Cauchy problem for the system of FIDEs on subintervals is obtained and by using a solution to this problem, a system of algebraic equations in parameters is constructed. An algorithm for solving the BVP and its computational implementation is developed. In the algorithm, Cauchy problems for ODEs and the calculation of definite integrals are the main auxiliary problems. By using various numerical methods for solving these auxiliary problems, the proposed algorithm can be implemented in different ways. The program codes were written to solve the problem and all calculations are performed on the Matlab 2018 software platform.
脉冲积分微分方程边值问题的一种计算方法
在本文中,我们感兴趣的是找到具有退化核的Fredholm IDE在脉冲作用下的线性BVP的数值解。利用Dzumabaev的参数化方法,将带有附加参数的Fredholm IDE系统的原始问题简化为多点BVP。对于固定参数,得到了子区间FIDE系统的特殊Cauchy问题,并利用该问题的解构造了参数代数方程组。提出了一种求解BVP的算法及其计算实现。在算法中,常微分方程的柯西问题和定积分的计算是主要的辅助问题。通过使用各种数值方法来解决这些辅助问题,所提出的算法可以以不同的方式实现。编写了解决该问题的程序代码,所有计算都在Matlab 2018软件平台上进行。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.30
自引率
0.00%
发文量
11
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