| 基于二分法求解一类函数方程的数值解 |
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| 引用本文： | 刘高峰,邵军.基于二分法求解一类函数方程的数值解[J].内江师范学院学报,2010,25(4):14-16. |
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| 作者姓名： | 刘高峰 邵军 |
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| 作者单位： | 1. 内江师范学院数学与信息科学学院,四川,内江,641100;四川省高等学校数值仿真重点实验室,四川,内江,641100
2. 内江师范学院数学与信息科学学院,四川,内江,641100 |
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| 基金项目： | 四川省教育厅青年基金(07ZB043) |
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| 摘 要： | 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．
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| 关 键 词： | 函数方程 二分法 数值解 |
Determination of the Numerical Solution to Functional Equations of First Kind Based on Dichotomy |
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| LIU Gao-feng,SHAO Jun.Determination of the Numerical Solution to Functional Equations of First Kind Based on Dichotomy[J].Journal of Neijiang Teachers College,2010,25(4):14-16. |
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| Authors: | LIU Gao-feng SHAO Jun |
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| Institution: | 1.College of Mathematics & Information Sciences/a>;Neijiang Normal University/a>;Neijiang/a>;Sichuan 641000/a>;China/a>;2.Key Laboratory for Numerical Simulation of Sichuan Province/a>;China |
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| Abstract: | 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 nu... |
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| Keywords: | functional equation numerical solution dichotomy |
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