A numerical study of singularly perturbed generalized Burgers–Huxley equation using three-step Taylor–Galerkin method

Abstract

In the present work, a numerical study has been carried out for the singularly perturbed generalized Burgers–Huxley equation using a three-step Taylor–Galerkin finite element method. A Burgers–Huxley equation represents the traveling wave phenomena. In singular perturbed problems, a very small positive parameter, ϵ , called the singular perturbation parameter is multiplied with the highest order derivative term. As this parameter tends towards zero, the problem exhibits boundary layers. The traditional methods fail to capture the boundary layers when ϵ becomes very small. In this paper a three-step Taylor–Galerkin finite element method is used to capture the boundary layers. The method is third-order accurate and has inbuilt upwinding. Stability analysis has been carried out and the numerical results show that the method is efficient in capturing the boundary layers.