Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids

Authors:
M. K. Kadalbajoo;K. C. Patidar
Affiliations:
Professor, Department of Matematics, Indian Institute of Technology, Kanpur, India;Research Scholar, Department of Mathematics, Indian Institute of Technology, Kanpur, India
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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Abstract

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems, The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.