TY - JOUR
T1 - A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology
AU - M. Abukhaled, S. A. Khuri & A. Sayfy
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 - <p style="text-align: justify;">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&#39;Hopital&#39;s rule is used to remove the singularity due to
the boundary condition (BC) $y&#39;(0) = 0$. 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.</p>