Accelerated nonstandard finite difference method for singularly perturbed Burger-Huxley equations

Abstract

Objective The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. Results The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.

Second-order robust finite difference method for singularly perturbed Burgers' equation

“…Then as indicated in Eq. (5.3) , the error estimate is given by Therefore, the formulated method is a consistent and stable scheme that implies convergent scheme by Lax's equivalence, [6] , [25] , [26] .…”

“…Therefore, the formulated method is a consistent and stable scheme that implies convergent scheme by Lax's equivalence, [6], [25], [26].…”

Uniformly convergent computational method for singularly perturbed unsteady burger-huxley equation

“…To linearize the semi-linear term of Eq. (1.1) , we choose the reasonable initial approximation for the function in the term , and denote it as that satisfy both initial and boundary conditions which is obtained by separation of variables method of the homogeneous part of the problem under consideration and is given by [13] : Thus, the nonlinear term of Eq. (3.1) can be linearized by applying the Newton-Raphson- Kantorovich approximation approach as Substitution of Eq.…”

“…(1.1) is suggested by [23] . [12] , [13] considered a similar problem as in [23] and proposed a parameter uniform numerical method based on fitted operator techniques. Very recently, [3] developed fitted operator finite difference method for singularly perturbed Burgers’ initial-boundary value problem.…”

“…The methods developed by [7] , [12] , [13] , [14] , [23] for Eq. (1.1) are based on finite difference method.…”