求解对流扩散方程的紧致二级四阶Runge-Kutta差分格式

将指数变换u(x,t)=p(x,t)exp(k2εx)应用于一维对流扩散方程,对空间变量x应用紧致差分格式,时间变量t采用二级四阶Runge-Kutta方法,提出了精度为o(τ4+h4)的绝对稳定的差分格式,讨论了稳定性.最后通过数值算例说明该格式的有效性.

A compact two stage fourth order runge- kutta method scheme for solving convection diffusion equation

In this note the absolutely stabilized difference scheme with accuracy o( τ4+ h4) is given for one dimensional convection diffusion equation by the way of using exponential transformu( x,t) = p( x,t) exp(k2εx),p( x,t) =v( x,t) exp( at),compact finite difference approximation of fouth order for spatial derivatives,and two stage fourth order Runge- Kutta method in time direction. And the efficiency of the scheme is showed by a numerical example at the end of this note.