A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology
Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 2 : pp. 353–363
Abstract
In this paper, two numerical schemes for finding approximate solutions of singular two-point 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-689
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 2 : pp. 353–363
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Boundary value problems Chebyshev polynomial B-spline singularities.