Singularly perturbative behaviour of nonlinear advection-diffusion-reaction processes

Abstract

The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE's behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. The wavelet method is seen to be very capable of solving a singularly perturbed nonlinear process without linearization by utilizing multi-resolution features. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection-diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.