Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids |
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| Authors: | Kadalbajoo MK Patidar KC |
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| Institution: | (1) Department of Mathematics, Indian Institute of Technology, Kanpur, India;(2) Department of Mathematics, Indian Institute of Technology, Kanpur, India |
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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. |
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| Keywords: | singular perturbations boundary-value problems ordinary differential equations cubic splines quasilinearization |
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