Browsing by Author "Eryilmaz, Aytekin"

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Magnus series expansion method for solving nonhomogeneous stiff systems of ordinary differential equations
(ACADEMIC PUBLICATION COUNCILPO BOX 17225, KHALDIYA 72453, KUWAIT, 2016) Atay, Mehmet T.; Eryilmaz, Aytekin; Komez, Sure; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü; Atay, Mehmet T.
In this paper, Magnus Series Expansion Method, which is based on Lie Groups and Lie algebras is proposed with different orders to solve nonhomogeneous stiff systems of ordinary differential equations. Using multivariate Gaussian quadrature, fourth (MG4) and sixth (MG6) order method are presented. Then, it is applied to nonhomogeneous stiff systems using different step sizes and stiffness ratios. In addition, approximate and exact solutions are demonstrated with figures in detail. Moreover, absolute errors are illustrated with detailed tables.
A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions
(SPRINGER INTERNATIONAL PUBLISHING AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND, 2016) Cengizci, Suleyman; Atay, Mehmet Tarik; Eryilmaz, Aytekin; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü;
This 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.