Fredholm积分方程的数值格式

A. Nazemi, M. H. Farahi
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引用次数: 1

摘要

考虑了求解第二类连续核非线性Fredholm积分方程的一种不同的数值方法。其主要思想是将积分方程问题转化为优化问题。然后利用嵌入方法,将可容许轨迹类替换为正Borel测度类。然后将测度空间中的优化问题近似化为有限维线性规划问题。算例验证了该方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A numerical scheme for Fredholm integral equations
A different numerical method for nonlinear Fredholm integral equations of the second kind with the continuous kernel is considered. The main idea is to convert the integral equation problem into an optimization problem. Then by using an embedding method, the class of admissible trajectories is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a finite dimensional linear programming (LP) problem. Some examples demonstrate the effectiveness of the method.
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