Analysis of IVPs and BVPs on Semi-Infinite Domains via Collocation Methods. (20th March 2012) - Maleki, Mohammad
Abstract : 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 domainx ∈ [ 0, ∞ ) onto a half-open intervalt ∈ [ − 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 mapϕ : [ − 1, + 1 ) → [ 0, + ∞ ) and its effects on the quality of the discrete approximation are analyzed.