A modified exponential method that preserves structural properties of the solutions of the Burgers–Huxley equation

Abstract

ABSTRACTIn this work, we consider the classical Burgers–Huxley partial differential equation defined on a closed and bounded interval of the real line. For this model, theorems on the existence and uniqueness of positive and bounded solutions are readily at hand, whence the design of positivity- and boundedness-preserving numerical methods is pragmatically justified. In this manuscript, we propose a monotone and explicit numerical technique that preserves the structure of such solutions. The method proposed here is a correction of the well-known Bhattacharya method to avoid the presence of singularities. The scheme is an explicit technique, and the simulations confirm in the practice that the structural properties of interest are preserved. Moreover, the computer results yield good approximations to the exact travelling-wave solutions considered here.