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

Mohammad Maleki, Ishak Hashim and Saeid Abbasbandy

Journal of Applied Mathematics, 2012, vol. 2012, 1-21

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 𠑥 ∈ [ 0 , ∞ ) onto a half-open interval 𠑡 ∈ [ − 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 𠜙 ∶ [ − 1 , + 1 ) → [ 0 , + ∞ ) and its effects on the quality of the discrete approximation are analyzed.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:696574

DOI: 10.1155/2012/696574

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