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Numerical studies on 2-dimensional reaction-diffusion equations

Published online by Cambridge University Press:  17 February 2009

S. Tang ,
S. Qin  and
R. O. Weber
S. Tang
Affiliation:
Dept of Mechanics, Peking University, Beijing 100871, China
S. Qin
Affiliation:
Dept of Mechanics, Peking University, Beijing 100871, China
R. O. Weber
Affiliation:
Dept of Mathematics, University of NSW, ADFA, Canberra ACT 2600, Australia
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Abstract

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Various initial and boundary value problems for a 2-dimensional reaction-diffusion equation are studied numerically by an explicit Finite Difference Method (FDM), a Galerkin and a Petrov-Galerkin Finite Element Method (FEM). The results not only show the transition processes from different local initial disturbances to quasitravelling waves, but also demonstrate the long term behaviour of the solutions, which is determined by the system itself and does not depend on the details of the initial disturbances.

Type
Research Article
Information
The ANZIAM Journal , Volume 35 , Issue 2 , October 1993 , pp. 223 - 243
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Argyris, J., Haase, M. and Heinrich, J. C., “Finite approximation to two-dimensional sine-Gordon equations”, Computer Methods in Appl. Mech. and Eng. 86 (1991) 1–26.CrossRefGoogle Scholar
[2]Aronson, D. G. and Weinberger, H. F., “Multidimensional nonlinear diffusion arising in population genetics”, Advance in Mathematics 30 (1978) 33–76.CrossRefGoogle Scholar
[3]Grimshaw, R. and Tang, S., “The rotation-modified Kadomtsev-Petviashvili equation: an analytical and numerical study”, Studies in Appl. Math. 83 (1990) 223–248.CrossRefGoogle Scholar
[4]Tang, S., Qin, S. and Weber, R. O., “Numerical solution of a nonlinear reaction-diffusion equation”, Chinese J. of Appl. Math. and Mech. 12 (8) (1991), Chinese Edition pp. 703–709; English Edition pp.751–758.Google Scholar
[5]Tang, S. and Weber, R. O., “Numerical study of Fisher's equation by a Petrov-Galerkin finite element method”, J. of Austral. Math. Soc. Series B 33 (1991) 27–38.CrossRefGoogle Scholar