Journal of innovative applied mathematics and computational sciences
Volume 3, Numéro 2, Pages 121-141
2024-01-21
On Numerical And Analytical Solutions Of The Generalized Burgers-fisher Equation
Authors : Lukonde Japhet . Kasumo Christian .
Abstract
In this paper, the semi-analytic iterative and modified simple equation methods have been implemented to obtain solutions of the generalized Burgers-Fisher equation. To demonstrate the accuracy, efficacy as well as reliability of the methods in finding the exact solution of the equation, a selection of numerical examples were given and a comparison was made with other well-known methods from the literature such as variational iteration method, homotopy perturbation method and diagonally implicit Runge-Kutta method. The results have shown that between the proposed methods, the modified simple equation method is much faster, easier, more concise and straightforward for solving nonlinear partial differential equations as it does not require the use of any symbolic computation software such as Maple or Mathematica. Additionally, the iterative procedure of the semi-analytic iterative method has merit in that each solution is an improvement of the previous iterate and as more and more iterations are taken, the solution converges to the exact solution of the equation.
Keywords
Generalized Burgers-Fisher equation ; Semi-analytic iterative method ; Modified simple equation method ; Diagonally implicit Runge-Kutta method ; Variational iteration method ; Homotopy perturbation method
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