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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

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

Abstract:

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.

Keywords: Diffusion equation, Exponential Time Difference Method, Runge-Kutta

DOI:

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