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Coupled ABC and Spline Collocation Approach for a Class of Nonlinear Boundary Value Problems over Semi-Infinite Domains

S.A. Khuri1, A. Sayfy1
1 Department of Mathematics and Statistics, American University of Sharjah - UAE.

Computer Modeling in Engineering & Sciences 2014, 101(2), 81-96. https://doi.org/10.3970/cmes.2014.101.081

Abstract

In this article, we introduce a numerical scheme to solve a class of nonlinear two-point BVPs on a semi-infinite domain that arise in engineering applications and the physical sciences. The strategy is based on replacing the boundary condition at infinity by an asymptotic boundary condition (ABC) specified over a finite interval that approaches the given value at infinity. Then, the problem complimented with the resulting ABC is solved using a fourth order spline collocation approach constructed over uniform meshes on the truncated domain. A number of test examples are considered to confirm the accuracy, efficient treatment of the boundary condition at infinity, and applicability of the approach. The computational results show that the scheme is reliable and converges fast with a fourth order rate of convergence

Keywords

Asymptotic boundary conditions, spline collocation, nonlinear twopoint BVPs

Cite This Article

Khuri, S., Sayfy, A. (2014). Coupled ABC and Spline Collocation Approach for a Class of Nonlinear Boundary Value Problems over Semi-Infinite Domains. CMES-Computer Modeling in Engineering & Sciences, 101(2), 81–96.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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