一个非线性偏微分方程边值问题的对称约化及其数值解

Abstract

本文研究了微分方程对称方法在非线性偏微分方程边值问题中的应用。首先，基于微分特征列集算法确定了给定非线性偏微分方程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边值问题化为常微分方程初值问题；最后，利用龙格-库塔法求解了常微分方程初值问题的数值解。 We study the applications of the symmetry method on the boundary value problem for nonlinear partial differential equation. Firstly, the multi-parameter symmetry of a given boundary value problem for nonlinear partial differential equation is determined based on differential characte-ristic set algorithm. Secondly, by using the symmetry, the boundary value problem for nonlinear partial differential equation is reduced to an initial value problem of the original differential equ-ation. Finally, we numerically solve the initial value problem of the original differential equations by using Runge-Kutta method.