﻿ 一个非线性偏微分方程边值问题的对称约化及其数值解

# 一个非线性偏微分方程边值问题的对称约化及其数值解Symmetry Reduction and Its Numerical Solution to the Boundary Value Problem of a Nonlinear Partial Differential Equation

Abstract: 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.

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