Asymptotic Initial-Value Method for Second-Order Singular Perturbation Problems of Reaction-Diffusion Type with Discontinuous Source Term

T. Valanarasu () and N. Ramanujam ()
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T. Valanarasu: Bharathidasan University
N. Ramanujam: Bharathidasan University

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 3, No 7, 383 pages

Abstract: Abstract In this paper, a numerical method is presented to solve singularly-perturbed two-point boundary-value problems for second-order ordinary differential equations with a discontinuous source term. First, an asymptotic expansion approximation of the solution of the boundary-value problem is constructed using the basic ideas of the well-known WKB perturbation method. Then, some initial-value problems and terminal-value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial-value problems and terminal-value problems are singularly-perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples are provided to illustrate the method.

Keywords: Singular perturbation problems; Discontinuous source terms; Boundary and interior layers; Asymptotic expansion approximations; Boundary value problems; Initial value problems; Initial value methods (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9167-3

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