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.