Journal of Applied Mathematics
Volume 2012 (2012), Article ID 696574, 21 pages
http://dx.doi.org/10.1155/2012/696574
Research Article

Analysis of IVPs and BVPs on Semi-Infinite Domains via Collocation Methods

Mohammad Maleki,1 Ishak Hashim,1 and Saeid Abbasbandy2

1School of Mathematical Sciences, National University of Malaysia (UKM), 43600 Bangi, Malaysia
2Department of Mathematics, Imam Khomeini International University, Ghazvin 34149-16818, Iran

Received 29 January 2012; Accepted 28 February 2012

Academic Editor: Md. Sazzad Chowdhury

Copyright © 2012 Mohammad Maleki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semi-infinite domain 𝑥 ∈ [ 0 , ∞ ) onto a half-open interval 𝑡 ∈ [ − 1 , 1 ) . The resulting finite-domain two-point boundary value problem is transcribed to a system of algebraic equations using Chebyshev-Gauss (CG) collocation, while the resulting initial value problem over a finite domain is transcribed to a system of algebraic equations using Chebyshev-Gauss-Radau (CGR) collocation. In numerical experiments, the tuning of the map 𝜙 ∶ [ − 1 , + 1 ) → [ 0 , + ∞ ) and its effects on the quality of the discrete approximation are analyzed.