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

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 semiinfinite domain x ∈ 0,∞ onto a half-open interval t ∈ −1, 1 . The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using ChebyshevGauss 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.