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解扩散方程的指数时间差分方法

孙建强1, 秦孟兆2, 戴桂冬3   

    1. 北京应用物理与计算数学研究所, 北京 100191
    2. 中国科学院计算数学研究所, 北京 100190
    3. 北京服装学院基础教学部, 北京 100029
  • 出版日期:2008-12-14 发布日期:2008-12-24
  • 基金资助:

    国家自然科学基金项目(10401033, 10471145)资助

孙建强, 秦孟兆, 戴桂冬. 解扩散方程的指数时间差分方法[J]. 数值计算与计算机应用, 2008, 29(4): 261-266.

Sun Jianqiang, Qin Mengzhao, Dai Guidong. EXPONENTIAL TIME DIFFERENCE METHOD TO SOLVE THE DIFFUSION EQUATION[J]. Journal of Numerical Methods and Computer Applications, 2008, 29(4): 261-266.

EXPONENTIAL TIME DIFFERENCE METHOD TO SOLVE THE DIFFUSION EQUATION

Sun Jianqiang1,  Qin Mengzhao2, Dai Guidong3   

    1. Institute of Applied Physics and Computational Mathematics, Beijing 100191, China
    2. Institute of Computational Mathematics, Chinese Academy of Science, Beijing 100190, China
    3. Element Department,Beijing Institute of FashionTechnology, Beijing 100029, China
  • Online:2008-12-14 Published:2008-12-24

指数时间差分方法是近年来提出求解刚性常微分方程的一种新的数值计算方法. 指数时间差分方法是一种积分方法,而不是经典的差分方法.
利用指数时间差分方法求解扩散方程,如一维拟线性对流扩散方程和Allen-Cahn扩散方程. 扩散方程在空间方向离散后转化成刚性常微分方程. 用显式指数时间差分方法和相应阶的显式 Runge-Kutta方法求解刚性常微分方程. 数值结果表明显式指数时间差分方法具有相同阶的显
式Runge-Kutta方法相应的精度,稳定性显著提高,而且能很好地模拟扩散方程的演化行为. 指数时间差分方法可用于刚性常微分方程的数值计算.

Exponential time difference method is a kind of new numerical computational method, which was proposed to solve the stiff ordinary differential equations recently. Exponential time difference method is a kind of integrator method, which  is not the classical difference method.
The diffusion equations, such as the one dimensional quasi-linear advection diffusion equation and the Allen-Cahn diffusion equation, were solved by the exponential time difference method. The diffusion equation was discretizated in the spacial direction and transformed into the stiff ordinary differential equations. The explicit exponential difference time method and the corresponding explicit Runge-Kutta method were applied to solve the stiff ordinary differential equations. Numerical results showed that  the explicit exponential time difference method has the same accuracy as the corresponding explicit Runge-Kutta method and better stability, moreover can well simulate the evolution behaviors of the diffusion equations.
The exponential time difference method can be applied to simulate the stiff ordinary differential equations.

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