摘要
提出一种求解非线性代数方程和非线性常微分方程的新方法．所论方程组被转换成增量形式，而解被表示成泰勒级数．在代数方程（多项式形式）的情况下，此算法归结为求解一系列线性方程组，而且在每一增量步中系数矩阵是不变的；在常微分方程组的情况下，此算法归结为一组递归算式，并不要求解方程组．此方法固有的自动走步功能，可保证得到收敛的解。
A new approach for solution of nonlinear algebraic and differential equation sets was presented.The sets were transferred into incremental form and their solutions into Taylor expansions.In the case of algebraic(polynomial form)equation,the method turns out to be one dealing with a series of linear equation sets with the same coefficients.In the case of ordinary differential equation,it gives a group of recursive formulas and no simultaneous solution is required.An advantage of inherent auto-stepping of this method can insure convergence of the solution and save CPU time.
出处
《北京航空航天大学学报》
EI
CAS
CSCD
北大核心
1996年第3期326-331,共6页
Journal of Beijing University of Aeronautics and Astronautics
基金
航空科学基金
关键词
泰勒级数
代数方程
微分方程
方程组
非线性
Taylor series
algebraic functions
differential equation
simultaneous equations
non linear
