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Applied Mathematics and Mechanics (English Edition) ›› 1991, Vol. 12 ›› Issue (8): 751-758.

• 论文 • 上一篇    下一篇

NUMERICAL SOLUTION OF A NONLINEAR REACTION-DIFFUSION EQUATION

唐世敏1, 秦素娣1, R.O.Weber2   

  1. 1. Peking University, Beijing;
    2. The University of New South Wales, Australia
  • 收稿日期:1990-08-20 出版日期:1991-08-18 发布日期:1991-08-18

NUMERICAL SOLUTION OF A NONLINEAR REACTION-DIFFUSION EQUATION

Tang Shi-min1, Qin Su-di1, R. O. Weber2   

  1. 1. Peking University, Beijing;
    2. The University of New South Wales, Australia
  • Received:1990-08-20 Online:1991-08-18 Published:1991-08-18

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摘要： A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space. The comparison between the exact and numerical solutions of progressive waves shows that this numerical scheme is quite accurate, stable andefflcient. It is also shown that any local disturbance will spread, have a full growth and finally form two progressive waves propagating in both directions. The shape and the speed of the long term progressive waves are determined by the system itself, and do not depend on the details of the initial values.

关键词: reaction-diffusion equation, Petrov-Galerkin finite element method, progressive wave

Abstract: A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space. The comparison between the exact and numerical solutions of progressive waves shows that this numerical scheme is quite accurate, stable andefflcient. It is also shown that any local disturbance will spread, have a full growth and finally form two progressive waves propagating in both directions. The shape and the speed of the long term progressive waves are determined by the system itself, and do not depend on the details of the initial values.

Key words: reaction-diffusion equation, Petrov-Galerkin finite element method, progressive wave

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