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

S. Tang; R. O. Weber

doi:10.1017/s0334270000008602

journal article Jul 01, 1991

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

S. Tang

R. O. Weber

The Journal of the Australian Mathematical Society. Series B. Applied Mathematics Vol. 33 No. 1 pp. 27-38 · Cambridge University Press (CUP)

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Abstract

AbstractFisher'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.

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References

13

[1]

Zeldovich "A theory of thermal propagation of flame" Acta Physicochimica U.R.S.S. (1938)

[2]

Tang "Numerical study on regularized long wave equations" Chinese Journal of Computational Physis (1989)

[3]

[6] Grimshaw R. and Tang S. , “The rotation-modified Kadomtsev-Petviashvili equation: an analytical and numerical study” (submitted) (1989). 10.1002/sapm1990833223

[4]

THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES

R. A. Fisher

Annals of Eugenics 10.1111/j.1469-1809.1937.tb02153.x

[5]

10.2307/3212689

[6]

Sun "Analytical and numerical studies on interaction of solitons of Modified KdV equations" Chinese Journal of Computational Physics

[7]

On a Nonlinear Diffusion Equation Describing Population Growth

Jose Canosa

IBM Journal of Research and Development 10.1147/rd.174.0307

[8]

Kolmogoroff "Study of the diffusion equation with growth of the quantity of matter and its application to biology problem" Bulletin de l'Université d'élat ὰ Moscou, Série Internationale, Section A (1937)

[9]

Smith (1978)

[10]

10.1063/1.1664771

[11]

Tang "Numerical study on KdV solitons and their interactions by a Petrov-Galerkin finite element method" Acta Mechanica (1989)

[12]

Evans "The alternating group explicit (AGE) iterative method to solve parabolic and hyperbolic partial differential equations" Ann. of Numerical Fluid Mechanics and Heat Transfer (1989)

[13]

10.1017/cbo9780511569449

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Details

Published: Jul 01, 1991
Vol/Issue: 33(1)
Pages: 27-38
License: View

Authors

Cite This Article

S. Tang, R. O. Weber (1991). Numerical study of Fisher's equation by a Petrov-Galerkin finite element method. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 33(1), 27-38. https://doi.org/10.1017/s0334270000008602

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

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