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 onto a half-open interval . 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 and its effects on the quality of the discrete approximation are analyzed.
Mohammad Maleki. Ishak Hashim. Saeid Abbasbandy. "Analysis of IVPs and BVPs on Semi-Infinite Domains via Collocation Methods." J. Appl. Math. 2012 1 - 21, 2012. https://doi.org/10.1155/2012/696574