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Volume 8, Issue 2
A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology

M. Abukhaled, S. A. Khuri & A. Sayfy

Int. J. Numer. Anal. Mod., 8 (2011), pp. 353-363.

Published online: 2011-08

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  • 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.

  • Keywords

Boundary value problems, Chebyshev polynomial, B-spline, singularities.

  • AMS Subject Headings

65L10, 65L11, 65D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-353, author = {M. Abukhaled, S. A. Khuri and A. Sayfy}, title = {A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {2}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/689.html} }
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 -

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.

M. Abukhaled, S. A. Khuri and A. Sayfy. (2011). A Numerical Approach for Solving a Class of a Singular Boundary Value Problems Arising in Physiology. International Journal of Numerical Analysis and Modeling. 8 (2). 353-363. doi:
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