Abstract
In this paper, we obtain the numerical solution of a 1-D generalised Burgers-Huxley equation under specified initial and boundary conditions, considered in three different regimes. The methods are Forward Time Central Space (FTCS) and a non-standard finite difference scheme (NSFD). We showed the schemes satisfy the generic requirements of the finite difference method in solving a particular problem. There are two proposed solutions for this problem and we show that one of the proposed solutions contains a minor error. We present results using FTCS, NSFD, and exact solution as well as show how the profiles differ when the two proposed solutions are used. In this problem, the boundary conditions are obtained from the proposed solutions. Error analysis and convergence tests are performed.
Highlights
The study of nonlinear partial differential equation continues to fascinate many researchers due to their ubiquitous application in every area of science and technology
The use and popularity of the non-standard finite difference scheme (NSFD) scheme are due to anomalous behaviour of the traditional finite difference scheme when used in discretisation of some continuous differential equation
We examined the two proposed solutions provided by Wang et al [8] and Deng [19] for the generalised BurgersHuxley equation
Summary
The study of nonlinear partial differential equation continues to fascinate many researchers due to their ubiquitous application in every area of science and technology. Some analyses of most numerical and semi-analytical methods are studied using the heat equation The linearity of this differential equation makes it a test case for many problems, it takes the form. Many drawbacks of the approximation analytical approaches include slow convergence at long propagation t, expensive computer memory usage, and difficulty in finding a closed form formula for the resulting series expression ([9, 10]). To this end, we cannot overemphasise the need for analysing the two proposed solutions from Wang et al [8] and Deng [19]. We will obtain solution of the generalised Burgers-Huxley equation using the classical finite difference scheme (FTCS) and non-standard finite difference scheme (NSFD)
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
