WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Article Citation - WoS: 3Citation - Scopus: 3A Uniformly Valid Approximation Algorithm for Nonlinear Ordinary Singular Perturbation Problems With Boundary Layer Solutions(Springer int Publ Ag, 2016-03-05) Cengizci, Suleyman; Atay, Mehmet Tarik; Eryilmaz, AytekinThis paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.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.