The Journal of the Australian Mathematical Society. Series B. Applied Mathematics

Research Article

Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

S. Tanga1 and R. O. Webera2

a1 Department of Mechanics, Peking University, Beijing 100871, China.

a2 Department of Mathematics, Australian Defence Force Academy, Canberra ACT 2600.

Abstract

Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

(Received May 16 1990)

(Revised August 28 1990)