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, issue 1

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.

Date: 2012
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https://doi.org/10.1155/2012/696574

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:696574

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