Rosenau-Burgers方程一种新的数值解法

A New Numerical Method for Rosenau-Burgers Equation

本文讨论Rosenau-Burgers方程初边值问题的数值解法.针对Rosenau-Burgers方程构造了一个新的差分格式,把网格分为奇、偶两套独立的网格,在偶数网格点采用显式格式,在奇数网格点采用Crank-Nicolson格式,这样偶、奇、显、隐交替的方法使计算量减少.同时针对非线性项进行了线性化,使格式的近似解更精确.给出了稳定性和收敛性的严格理论证明,数值实验结果表明了理论证明的正确性及格式的有效性和可行性,具有推广价值.

In this paper,we discuss the numerical method of the initial-boundary value problem of Rosenau-Burgers equation.A new finite di？erence scheme is proposed for the Rosenau-Burgers equation.We separate the grid into the odd and the even parts,and apply the explicit scheme and Crank-Nicolson scheme at the even and the odd grid points,respectively.This scheme is easy to computation,and the approximation solutions are more accurate than transforming the nonlinear term into the linear term.The numerical experiment indicates the theoretical is accurate and the computation is effective,and the scheme is feasiable and worthy popularizing.