Spline solution of non-linear singular boundary value problems

Authors:
J. Rashidinia;R. Mohammadi;R. Jalilian
Affiliations:
School of Mathematics, Iran University of Science and Technology Narmak, Tehran, Iran;School of Mathematics, Iran University of Science and Technology Narmak, Tehran, Iran;School of Mathematics, Iran University of Science and Technology Narmak, Tehran, Iran
Venue:
International Journal of Computer Mathematics
Year:
2008

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Abstract

A class of non-linear singular boundary value problems is solved by new methods based on non-polynomial cubic spline. We use the quasilinearization technique to reduce the given non-linear problem to a sequence of linear problems. We modify the resulting set of differential equations at the singular point then treat this set of boundary value problems by using a non-polynomial cubic spline approximation. Convergence of the methods is shown through standard convergence analysis. Numerical examples are given to illustrate the applicability and efficiency of our methods.