Cengizci, SuleymanNatesan, SrinivasanAtay, Mehmet Tank2025-09-252025-09-2520191300-00981303-6149https://doi.org/10.3906/mat-1807-195https://search.trdizin.gov.tr/en/yayin/detay/336812/an-asymptotic-numerical-hybrid-method-for-singularly-perturbed-system-of-two-point-reaction-diffusion-boundary-value-problemshttps://hdl.handle.net/20.500.12573/3245Srinivasan, Natesan/0000-0001-7527-1989; Cengizci, Suleyman/0000-0002-4345-1253; Atay, Mehmet Tarik/0000-0002-7326-5750This 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.eninfo:eu-repo/semantics/closedAccessSingular Perturbation ProblemsReaction-Diffusion EquationsAsymptotic ApproximationsBoundary LayersFinite Difference MethodArticle10.3906/mat-1807-1952-s2.0-85061640402