## Analysis of IVPs and BVPs on semi-infinite domains via collocation methods.(English)Zbl 1244.76067

Summary: 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 $$x \in [0, \infty)$$ onto a half-open interval $$t \in [-1, 1)$$. 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 $$\phi : [-1, +1) \rightarrow [0, +\infty)$$ and its effects on the quality of the discrete approximation are analyzed.

### MSC:

 76M22 Spectral methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76S05 Flows in porous media; filtration; seepage
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