Computational and Applied Mathematics

, Volume 32, Issue 1, pp 163–177 | Cite as

A hybrid initial-value technique for singularly perturbed boundary value problems

Article

Abstract

In this paper, we propose a hybrid initial-value technique for singularly perturbed boundary value problems. First, we develop a hybrid scheme to solve the singularly perturbed initial-value problems, and then, the hybrid scheme is used to solve the singularly perturbed boundary value problems. The scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Necessary error estimates are derived for the scheme. To verify computational efficiency and accuracy, some numerical examples are provided.

Keywords

Asymptotic expansion approximation Backward difference operator Piecewise uniform Shishkin mesh Singularly perturbed boundary value problem Trapezoidal method 

Mathematics Subject Classification (2010)

Primary 65L11 Secondary 65L10 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013

Authors and Affiliations

  1. 1.SMCA, Thapar UniversityPatialaIndia
  2. 2.Department of Computer SciencePunjabi UniversityPatialaIndia

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