A numerical approach for solving a class of a singular boundary value problems arising in physiology
M. Abukhaled 1, S. A. Khuri 1, A. Sayfy 11 Department of Mathematics, American University of Sharjah, Sharjah, U.A.E.
Received by the editors February 16, 2010 and, in revised form, July 9, 2010.
In this paper, two numerical schemes for finding approximate solutions of singular twopoint boundary value problems arising in physiology are presented. While the main ingredient of both approaches is the employment of cubic B-splines, the obstacle of singularity has to be removed first. In the first approach, L'Hopital's rule is used to remove the singularity due to the boundary condition (BC) y'(0) = 0. In the second approach, the economized Chebyshev polynomial is implemented in the vicinity of the singular point due to the BC y(0) = A, where A is a constant. Numerical examples are presented to demonstrate the applicability and efficiency of the methods on one hand and to confirm the second order convergence on the other hand.AMS subject classifications: 65L10, 65L11, 65D07
Key words: Boundary value problems, Chebyshev polynomial, B-spline, singularities.
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