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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Kadalbajoo, M., Patidar, K. Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids. Journal of Optimization Theory and Applications 114, 573–591 (2002). https://doi.org/10.1023/A:1016023012671
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DOI: https://doi.org/10.1023/A:1016023012671