1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods

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.

A hybrid computational scheme for singularly perturbed Burgers’-Huxley equation

“…In the literature, regular Burgers’ Huxley equations are well solved in numerous research works, some of which can be referred in [5] , [7] , [8] , [9] , [10] , [14] , [15] , [19] , [20] , [21] , [22] , [24] , [25] , [26] for the detail discussions. However, very few parameter uniform numerical schemes are available for non-linear SPBHEs.…”

Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method

“…In addition, if we continue with the analogy in the chloride diffusion, it can be observed how the variation of the boundary conditions drastically modifies the chloride concentration in the concrete. Two more case studies will be presented below, in which the Riemann condition for initial conditions involving discontinuous values will be These types of problems are known as shock waves that propagate with the initial condition and where the boundary conditions are a function of the solution to the problem [50,52]. In these cases, the symmetry condition clearly cannot be applied; a space of unit length will be taken and will be divided into 1000 cells.…”

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

“…These methods include variational iteration method [34], variational iteration algorithm-I with an auxiliary parameter [3], the differential transform method [11], A fourth-order finite difference scheme [12], the discrete Adomian decomposition method [7], the residual power series [42], the finite difference method [23], non-polynomial cubic spline method [4], extended cubic B-spline approximation [6], finite-difference MacCormack method [17], C 1 Cubic quasi-interpolation splines [10], differential transform method and Padé approximant [43], double Laplace transform and double Laplace decomposition methods [31]. Many mathematicians have solved such problems to date, for more details, see [1,5,8,9,13,24,25,27,35]. Few authors have studied the spline method to solve partial differential equations, for instance, in [2,21,22,30,32,36,37,40].…”