Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids

M.K. Kadalbajoo and K.C. Patidar
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M.K. Kadalbajoo: Indian Institute of Technology
K.C. Patidar: Indian Institute of Technology

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 3, No 4, 573-591

Abstract: 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.

Keywords: singular perturbations; boundary-value problems; ordinary differential equations; cubic splines; quasilinearization (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1016023012671

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