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. © 2012 mohammad maleki et al.