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

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