Research ArticleOpen AccessGoogle Scholar indexed
Asymptotic Estimates for Second-Order Parameterized Singularly Perturbed Problem
Department of Mathematics, Faculty of Art and Science, Erzincan University, Erzincan, Turkey
- 1 Department of Mathematics, Faculty of Art and Science, Erzincan University, Erzincan, Turkey
Applied Mathematics·Volume 05 (2014)·Pages 1988–1992·Published 7 July 2014·DOI10.4236/am.2014.513191
Copy link · social · email
Abstract
The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.
KeywordsParameterized ProblemAsymptotic BoundsSingular PerturbationBoundary Layer
- Pomentale, T. (1976) A Constructive Theorem of Existence and Uniqueness for the Problem. Zeitschrift für Angewandte Mathematik und Mechanik, 56, 387-388. http://dx.doi.org/10.1002/zamm.19760560806
- Goma, I.A. (1977) Method of Successive Approximations in a Two-Point Boundary Problem with Parameter. Ukrainian Mathematical Journal, 29, 594-599. http://dx.doi.org/10.1007/BF01085968
- Jankowski, T. (2001) Monotone ?terations for Differential Problems. Miskolc Mathematical Notes, 2, 31-38.
- Jankowski, T. and Lakshmikantham, V. (1997) Monotone Iterations for Differential Equations with a Parameter. Journal of Applied Mathematics and Stochastic Analysis, 10, 273-278. http://dx.doi.org/10.1155/S1048953397000348
- Jankowski, T. (1999) Generalization of the Method of Quasilinearization for Differential Problems with a Parameter, Dynamic Systems an Applications, 8, 53-72.
- Rontó, M. and Csikos-Marinets, T. (2000) On the Investigation of Some Non-Linear Boundary Value Problems with Parameters. Miskolc Mathematical Notes, 1, 157-166.
- Rontó, M. (2000) On Non-Linear Boundary Value Problems Containing Parameters. Archivum Mathematicum, 36, 585-593.
- Staněk, S. (1997) Nonlinear Boundary Value Problem for Second Order Differential Equations Depending on a Parameter. Mathematica Slovaca, 47, 439-449.
- Zhang, P. (2011) Existence of Positive Solutions for Nonlocal Second-Order Boundary Value Problem with Variable Parameter in Banach Spaces. Fixed Point Theory and Applications, 43, 1687-1812. http://dx.doi.org/10.1186/1687-1812-2011-43
- Fěckan, M. (1994) Parametrized Singularly Perturbed Boundary Value Problems. Journal of Mathematical Analysis and Applications, 188, 426-435. http://dx.doi.org/10.1006/jmaa.1994.1436
- Amiraliyev, G.M., Kudu M. and Duru, H. (2004) F?n?te-Difference Method for Parameter?zed S?ngularly Pertur Bed Problem. Journal of Applied Mathematics, 3, 191-199. http://dx.doi.org/10.1155/S1110757X0440103X
- Amiraliyev, G.M., Kudu M. and Duru, H. (2006) Uniform Difference Method for a Parameterized Singular Pertur Bation Problem. Applied Mathematics and Computation, 175, 89-100. http://dx.doi.org/10.1016/j.amc.2005.07.068
- Amiraliyeva I.G. and Amiraliyev, G.M. (2009) Uniform Difference Method for Parameterized Singularly Pertur Bed Delay Differential Equations. Numerical Algorithms, 52, 509-552. http://dx.doi.org/10.1007/s11075-009-9295-y