An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems

Authors : Süleyman CENGİZCİ, Srinivasan NATESAN, Mehmet Tarik ATAY

Pages : 460-472

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Publication Date : 0000-00-00

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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