The analysis of the solution of the Burgers–Huxley equation using the Galerkin method

Abstract

AbstractMany scientific methods have been proposed to solve the Burgers–Huxley equation. Among these famous methods, little or nothing has been mentioned in the literature about the coupling of the nonstandard finite difference method in the time and the Galerkin together with the compactness methods in the space variables. We exploit this gap and present a reliable technique aimed to use this coupling technique and show that the solution of the problem under investigation is uniqued in appropriate spaces to be defined. We proceed to show that the numerical solution obtained from the designed scheme is stabled and converges in the as well as the H1‐norms. Furthermore, we use examples together with some numerical experiments to justify the validity of our theoretical results.