caa a22 4500 463169034 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s10957-007-9200-6 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9200-6 B-Spline Collocation Method for Nonlinear Singularly-Perturbed Two-Point Boundary-Value Problems [Elektronische Daten] [S. Rao, M. Kumar] A B-spline collocation method is presented for nonlinear singularly-perturbed boundary-value problems with mixed boundary conditions. The quasilinearization technique is used to linearize the original nonlinear singular perturbation problem into a sequence of linear singular perturbation problems. The B-spline collocation method on piecewise uniform mesh is derived for the linear case and is used to solve each linear singular perturbation problem obtained through quasilinearization. The fitted mesh technique is employed to generate a piecewise uniform mesh, condensed in the neighborhood of the boundary layers. The convergence analysis is given and the method is shown to have second-order uniform convergence. The stability of the B-spline collocation system is discussed. Numerical experiments are conducted to demonstrate the efficiency of the method. Springer Science+Business Media, LLC, 2007 Singular perturbations nationallicence Boundary-value problems nationallicence B-spline collocation method nationallicence Piecewise uniform mesh nationallicence Quasilinearization nationallicence Rao S. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India aut Kumar M. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 134/1(2007-07-01), 91-105 0022-3239 134:1<91 2007 134 10957 https://doi.org/10.1007/s10957-007-9200-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9200-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rao S. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India aut NATIONALLICENCE 700 1- Kumar M. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 134/1(2007-07-01), 91-105 0022-3239 134:1<91 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer