Browsing by Author "Cengizci, Suleyman"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    Article
    An asymptotic-numerical hybrid method for singularly perturbed system of two-point reaction-diffusion boundary-value problems
    (SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, ATATURK BULVARI NO 221, KAVAKLIDERE, TR-06100 ANKARA, TURKEY, 2019) Cengizci, Suleyman; Natesan, Srinivasan; Atay, Mehmet Tank; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü;
    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 (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.
  • Thumbnail Image
    Article
    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.