- Turkish Journal of Mathematics
- Vol: 43 Issue: 1
- An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusio...
An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems
Authors : Süleyman Cengizci, Srinivasan Natesan, Mehmet Tarik Atay
Pages : 460-472
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.Keywords : Singular perturbation problems, reaction-diffusion equations, asymptotic approximations, boundary layers, finite difference method