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Kaya, Doǧan; El-Sayed, Salah M.

A numerical simulation and explicit solutions of the generalized Burgers–Fisher equation. (English) Zbl 1052.65098

Appl. Math. Comput. 152, No. 2, 403-413 (2004).
The authors present a method for the solution of a Burgers equation with a Fisher source term by computing terms of a series. The method requires that the solution possess a very high degree of regularity, namely, the condition that \(\| \partial_x^2 u \| \leq M \| u \| \). The method is very effective in special cases, such as that presented here.
Reviewer: Gerald W. Hedstrom (Pleasanton)

Cited in 40 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

Burgers-Fisher equation; series solution; decomposition method; solitary-wave solution; numerical results

Software:

ATFM
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Full Text: DOI

References:

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[29] S.M. El-Sayed, D. Kaya, An application of the ADM to seven-order Sawada-Kotare equations, submitted for publication; S.M. El-Sayed, D. Kaya, An application of the ADM to seven-order Sawada-Kotare equations, submitted for publication
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