title: A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.
abstract: 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.
authors.affiliation: Institute of Applied Mathematics, Middle East Technical University, 06800 Ankara, Turkey.
authors.forename: Süleyman
authors.identifier: 0000-0002-4345-1253
authors.initials: S
authors.lastname: Cengizci
authors.affiliation: Department of Mechanical Engineering, Abdullah Gül University, 38039 Kayseri, Turkey.
authors.forename: Mehmet Tarık
authors.initials: MT
authors.lastname: Atay
authors.affiliation: Department of Mathematics, Nevşehir Hacı  Bektaş Veli University, 50300 Nevşehir, Turkey.
authors.forename: Aytekin
authors.initials: A
authors.lastname: Eryılmaz
keywords: Asymptotic expansion; Boundary layer; Singular perturbation; Successive Complementary Expansion Method; Uniformly valid approximation