利用对称方法求解非线性偏微分方程组边值问题的数值解

Solve Numerical Solutions of Boundary Value Problem for Nonlinear Partial Differential Equations by Using Symmetry Method

本文研究微分方程对称方法在非线性偏微分方程组边值问题中的应用.首先,利用吴-微分特征列集算法确定给定非线性偏微分方程组边值问题的多参数对称;其次,利用对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解常微分方程组初值问题的数值解.

We study applications of the symmetry method on the boundary value problem for nonlinear partial differential equations.Firstly,by using Wu-differential characteristic set algorithm,the multiparameter symmetry of a given boundary value problem for nonlinear partial differential equations are proposed.Secondly,by using the symmetry,the boundary value problem for nonlinear partial differential equations is reduced to an initial value problem of the original differential equations.Finally,we solved numerical solutions of the initial value problem of the original differential equations by using Runge-Kutta method.