Abstract
A fourth order finite-difference scheme in a two-time level recurrence relation is proposed for the numerical solution of the generalized Burgers--Huxley equation. The resulting nonlinear system, which is analysed for stability, is solved using an improved predictor-corrector method. The efficiency of the proposed method is tested to the kink wave using both appropriate boundary values and conditions. The results arising from the experiments are compared with the relevant ones known in the available bibliography.
Highlights
IntroductionHuxley [1] proposed a model, known as the Huxley equation, in order to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon
A fourth order finite-difference scheme in a two-time level recurrence relation is proposed for the numerical solution of the generalized Burgers-Huxley equation
As far as the numerical methods are concerned among others the Adomian decomposition method was used by Ismail et al [12] for the Burgers-Huxley equation (BgH) and the Burgers-Fisher equation, and by Hashim et al [13] for the BgH equation
Summary
Huxley [1] proposed a model, known as the Huxley equation, in order to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. The most general form of the Huxley equation, known as the generalized Burgers-Huxley equation (BgH) [2,3], has the form [4]. Many researchers have used various methods to solve the BgH equation. A theoretical study of the BgH equation was found in Wang et al [4], while analytical solutions using various techniques in [7,8,9,10,11], etc., have been proposed. Theoretical Solution It is known [4] that Equation (1.1) has the following kink wave solution u.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
