A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions

Download

10.1186s40064-016-1865-6.pdf

Date

2016-3-5

Author

Cengizci, Süleyman
Atay, Mehmet Tarık
Eryılmaz, Aytekin

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

63
views

70
downloads

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.

Subject Keywords

Multidisciplinary, Uniformly valid approximation, Asymptotic expansion, Boundary layer, Singular perturbation, Successive Complementary Expansion Method

URI

https://hdl.handle.net/11511/52278

Journal

SpringerPlus

DOI

https://doi.org/10.1186/s40064-016-1865-6

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations Cengizci, Süleyman (Hindawi Limited, 2017) In thiswork, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, ...
On chaotic synchronization via impulsive control and piecewise constant arguments Mohamad S, Alwan; Xınzhı, Lıu; Akhmet, Marat (2015-01-01) This paper is concerned with a system of differential equations with continuous and piecewise constants arguments of a delay type. An application to chaotic systems is presented and the synchronization problem is established, where the output of the sender system, evaluated at the piecewise constant arguments, is transmitted to the receiver system. A global synchronization is achieved via impulsive effects, which are evaluated at the discrete arguments. The methodology of Lyapunov function together with lin...
Hamilton-Jacobi theory of discrete, regular constrained systems Güler, Y. (Springer Science and Business Media LLC, 1987-8) The Hamilton-Jacobi differential equation of a discrete system with constraint equationsG α=0 is constructed making use of Carathéodory’s equivalent Lagrangian method. Introduction of Lagrange’s multipliersλ˙α as generalized velocities enables us to treat the constraint functionsG α as the generalized momenta conjugate toλ˙α. Canonical equations of motion are determined.
DRBEM applications in fluid dynamics problems and DQM solutions of hyperbolic equations Pekmen, Bengisen; Tezer Sezgin, Münevver; Department of Scientific Computing (2014) In this thesis, problems of fluid dynamics defined by the two-dimensional convection-diffusion type partial differential equations (PDEs) are solved using the dual reciprocity boundary element method (DRBEM). The terms other than the Laplacian are treated as inhomogeneous terms in the DRBEM application. Once the both sides are multiplied by the fundamental solution of Laplace equation, and then integrated over the domain, all the domain integrals are transformed to boundary integrals using the Green's ident...
A SUPG Formulation for Solving a Class of Singularly Perturbed Steady Problems in 2D Cengizci, Süleyman; Uğur, Ömür; Srinivasan, Natesan (2020-09-02) In this presentation, approximate solutions of singularly perturbed partial differential equations are examined. It is a well-known fact that the standard Galerkin finite element method (GFEM) experiences some instability problems in obtaining accurate approximations to the solution of convection-dominated equations. Therefore, in this work, the Streamline-Upwind/Petrov-Galerkin (SUPG) method is employed to overcome the instability issues for the numerical solution of these kinds of problems. Furthermore,...

Citation Formats

S. Cengizci, M. T. Atay, and A. Eryılmaz, “A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions,” SpringerPlus, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52278.