Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/395
Browse
2 results
Search Results
Article Citation - WoS: 2Citation - Scopus: 3An Asymptotic-Numerical Hybrid Method for Singularly Perturbed System of Two-Point Reaction-Diffusion Boundary-Value Problems(Tubitak Scientific & Technological Research Council Turkey, 2019-01-18) Cengizci, Suleyman; Natesan, Srinivasan; Atay, Mehmet TankThis 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.Article Citation - WoS: 1Citation - Scopus: 2A Semi-Analytic Method for Solving Singularly Perturbed Twin-Layer Problems With a Turning Point(Vilnius Gediminas Tech Univ, 2023-01-19) Cengizci, Suleyman; Kumar, Devendra; Atay, Mehmet TarikThis computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving singularly perturbed differential equations as the perturbation (diffusion) parameter decreases, i.e., epsilon -> 0(+). To this end, this paper proposes a semi-analytic hybrid method consisting of a numerical procedure based on finite differences and an asymptotic method called the Successive Complementary Expansion Method (SCEM) to approximate the solution of such problems. Two numerical experiments are provided to demonstrate the method's implementation and to evaluate its computational performance. Several comparisons with the numerical results existing in the literature are also made. The numerical observations reveal that the hybrid method leads to good solution profiles and achieves this in only a few iterations.