TY - JOUR T1 - A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 353 EP - 363 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/689.html KW - Boundary value problems, Chebyshev polynomial, B-spline, singularities. AB -

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.