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Applied Mathematics and Mechanics

, Volume 12, Issue 8, pp 751–758 | Cite as

Numerical solution of a nonlinear reaction-diffusion equation

  • Tang Shi-min
  • Qin Su-di
  • R. O. Weber
Article

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 and efficient. 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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Copyright information

© SUT 1991

Authors and Affiliations

  • Tang Shi-min
    • 1
  • Qin Su-di
    • 1
  • R. O. Weber
    • 2
  1. 1.Peking UniversityBeijing
  2. 2.The University of New South WalesAustralia

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