求解对流扩散方程的紧致二级四阶 Runge-Kutta差分格式
A compact two stage fourth order runge-kutta methodscheme for solving convection diffusion equation
云南民族大学学报:自然科学版,2015,24(5):382-385

王慧蓉 WHR

摘要


将指数变换u(x,t)=p(x,t)exp((k2ε)x)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(τ4+h4)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. In this note the absolutely stabilized difference scheme with accuracy o(τ4+h4)is given for one dimensional convection diffusion equation by the way of using exponential transformu(x,t)=p(x,t)exp((k2ε)x),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.

参考



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