Fitted numerical method for singularly perturbed semilinear three-point boundary value problem

Iranian Journal of Numerical Analysis and Optimization

دوره 12، شماره 1 - شماره پیاپی 21، خرداد 2022، صفحه 145-162   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.70805.1040

نویسندگان

M. Gebeyehu؛ H. Garoma^* ؛ A. Deressa

Department of Mathematics, College of Natural Sciences,Jimma university, Jimma, Ethiopia.

چکیده

We consider a class of singularly perturbed semilinear three-point boundary value problems. An accelerated uniformly convergent numerical method is constructed via the exponential fitted operator method using Richardson extrapolation techniques to solve the problem. To treat the semilinear term, we use quasi-linearization techniques. The numerical results are tabulated in terms of maximum absolute errors and rate of convergence, and it is observed that the present method is more accurate and ε-uniformly convergent for h ≥ ε, where the classical numerical methods fail to give a good result. It also improves the results of the methods existing in the literature. The method is shown to be second-order convergent independent of perturbation parameter ε.

کلیدواژه‌ها

Singularly perturbed problem؛ Semilinear problem؛ Exponential fitted operator؛ Three-point boundary problem

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