A numerical simulation and explicit solutions of the generalized Burgers–Fisher equation

摘要

We consider solitary-wave solutions of the generalized Burgers–Fisher (BF) equation ut+purux−uxx−qu(1−ur)=0. In this paper by considering the decomposition scheme, we first obtain the exact solutions of the generalized BF equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Its remarkable accuracy is finally demonstrated in the study of some values r⩾2 of the generalized BF equation.