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 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.