caa a22 4500 463168879 CHVBK 20180406164807.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10957-007-9167-3 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9167-3 Asymptotic Initial-Value Method for Second-Order Singular Perturbation Problems of Reaction-Diffusion Type with Discontinuous SourceTerm [Elektronische Daten] [T. Valanarasu, N. Ramanujam] 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. Springer Science+Business Media, LLC, 2007 Singular perturbation problems nationallicence Discontinuous source terms nationallicence Boundary and interior layers nationallicence Asymptotic expansion approximations nationallicence Boundary value problems nationallicence Initial value problems nationallicence Initial value methods nationallicence Valanarasu T. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India aut Ramanujam N. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/3(2007-06-01), 371-383 0022-3239 133:3<371 2007 133 10957 https://doi.org/10.1007/s10957-007-9167-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9167-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Valanarasu T. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India aut NATIONALLICENCE 700 1- Ramanujam N. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/3(2007-06-01), 371-383 0022-3239 133:3<371 2007 133 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer