Rosenau-Burgers方程的一种新的二阶线性差分格式

A New Second-order Accurate Linearized Difference Scheme for the Rosenau-Burgers Equation

对于Rosenau-Burgers方程,提出了一种新的线性的三层差分格式,该格式在空间和时间上具有二阶精确.利用离散能量法证明差分解的收敛性和稳定性,并用数值实验验证该方法的可靠性.

A finite difference method for Rosenau-Burgers equation is considered.A linearized three level difference scheme,which is second order accurate in both space and time,is proposed.Convergence and stability of difference solution are proved by the means of discrete energy method.Numerical experiments validate that the method is reliable and spends less CPU time than the Crank-Nicolson scheme in implementation.