基于二分法求解一类函数方程的数值解

Determination of the Numerical Solution to Functional Equations of First Kind Based on Dichotomy

大多数函数方程的解析解是难以求解的,所以有必要研究函数方程高精度数值解的算法.针对一类函数方程,证明了它解的存在性与唯一性.基于二分法的思想提出了求解这类函数方程数值解的算法.经过理论分析与算例测试,对于任意给定的精度,都能求得满足精度要求的数值解.

Since the analytical solution to most functional Equations is rather hard to determine, it becomes quite necessary to research into the algorithm of high-degree-accuracy numerical solutions to the functional equations. For the functional equations of first kind, the existence of a unique solution is proved. Based on the concept of dichotomy, algorithm of the numerical solution to such functional equations is put forth. Through theoretical analysis and test of arithmetic examples, whatever an accuracy is given, a numerical solution of required-degree of accuracy can be obtained.