海南师范大学学报：自然科学版2012，Vol.25Issue(2)：119-121,3.
常微分方程初值问题的基本数值解法分析
Analysis of Basic Numerical Solutions for the Initial Value Problem of Ordinary Differential Equations
摘要
Abstract
The numerical solution of differential equations is widely used in science, technology, production practices and many other fields. This paper analyzed three kinds of basic methods for constructing numerical solutions for initial value problem of ordinary differential equations ： difference quotient instead of derivative method, numerical integral method and undetermined coefficients method. At the same time, the paper deduces the Euler series formula and the classical third order Runge-Kutta formula. In addition, the paper pointed out the advantages and disadvantages of each formula and application condition, it also analyzed the convergence and stability of the Euler formula.关键词
常微分方程/数值解法/收敛性/稳定性Key words
ordinary differential equations/numerical solution/convergence/stability分类
数学引用本文复制引用
林爽,张杰..常微分方程初值问题的基本数值解法分析[J].海南师范大学学报：自然科学版,2012,25(2):119-121,3.基金项目
国家自然科学基金资助项目 （）
