用泰勒级数求解非线性代数和微分方程组

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，从而大大节省计算时间。

SOLUTION OF NONLINEAR ALGEBRAIC AND DIFFERENTIAL EQUATION SETS VIA TAYLOR EXPANSION

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.