Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation
Publish place: Journal of Mathematical Modeling، Vol: 10، Issue: 4
Publish Year: 1401
Type: Journal paper
Language: English
View: 112
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Document National Code:
JR_JMMO-10-4_009
Index date: 8 June 2024
Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation abstract
We develop a robust uniformly convergent numerical scheme for singularly perturbed time dependent Burgers-Huxley partial differential equation. We first discretize the time derivative of the equation using the Crank-Nicolson finite difference method. Then, the resulting semi-discretized nonlinear ordinary differential equations are linearized using the quasilinearization technique, and finally, design a fitted operator upwind finite difference method to resolve the layer behavior of the solution in the spatial direction. Our analysis has shown that the presented method is second order parameter uniform convergent in time and first order in space. Numerical experiments are conducted to validate the theoretical results.
Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation Keywords:
Singularly perturbed problem , Burgers-Huxley equation , Crank-Nicolson finite difference scheme , fitted operator method , parameter uniform convergence
Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation authors
Eshetu Derzie
Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia
Justin B. Munyakazi
Department of Mathematics and Applied Mathematics, University of the Western Cape, Private BagX۱۷, Bellville ۷۵۳۵, South Africa
Tekle Dinka
Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia
