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

Daba, Imiru Takele; Duressa, Gemechis File

doi:10.1016/j.mex.2022.101886

Cited by 2 publications

(3 citation statements)

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“…These results show that the proposed scheme reveals the parameter uniform convergence of first order. Besides, the numerical results depict that the proposed method gives better results than those in [17][18][19]23]. The 3D view of the numerical solution of Examples 5.1 and 5.2 at N = 64, M = 40, and ε = 2 -18 are plotted in Fig.…”

Section: Numerical Examples Results and Discussionmentioning

confidence: 96%

“…Several model examples are presented to illustrate the efficiency of the proposed method. The proposed scheme gives more accurate numerical results than those in [17][18][19]23].…”

Section: Discussionmentioning

confidence: 92%

“…An upwind FDM on an adaptive nonuniform grid to find an approximate solution for problem (1) is suggested by Liu et al [19]. In [20][21][22][23] the authors proposed a parameter uniform numerical method based on fitted operator techniques for problem (1).…”

Section: Introductionmentioning

confidence: 99%

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Fitted numerical method for singularly perturbed Burger–Huxley equation

Daba

Duressa²

2022

Bound Value Probl

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This paper deals with the numerical treatment of a singularly perturbed unsteady Burger–Huxley equation. We linearize the problem using the Newton–Raphson–Kantorovich approximation method. We discretize the resulting linear problem using the implicit Euler method and specially fitted finite difference method for time and space variables, respectively. We provide the stability and convergence analysis of the method, which is first-order parameter uniform convergent. We present several model examples to illustrate the efficiency of the proposed method. The numerical results depict that the present method is more convergent than some methods available in the literature.

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Section: Numerical Examples Results and Discussionmentioning

confidence: 96%

“…Several model examples are presented to illustrate the efficiency of the proposed method. The proposed scheme gives more accurate numerical results than those in [17][18][19]23].…”

Section: Discussionmentioning

confidence: 92%