The authors consider Fisher’s equation \((1)\quad u_ t=\alpha u_{xx}+\beta u(1-u)\) which describes the propagation of a virile mutant in an infinitely long habitat or represents a model equation for the evolution of a neutron population in a nuclear reactor. A variables transformation leads to \((2)\quad u_{\tau}=u_{\xi \xi}+u(1-u)\) and the authors are looking for a travelling wave solution satisfying: \(u(\xi,\tau)=u(\xi -c\tau).\) For solving equation (2) a Petrov-Galerkin finite element method is introduced. Cubic spline functions are used for approximating the solution of (1). Interesting numerical developments are given.
It would be of interest to compare the authors’ numerical method with Adomian’s technique for solving nonlinear functional equations.