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**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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\textit{M. Maleki} et al., J. Appl. Math. 2012, Article ID 696574, 21 p. (2012; Zbl 1244.76067)

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### References:

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