### 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 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.

Original language | English |
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Article number | 696574 |

Journal | Journal of Applied Mathematics |

Volume | 2012 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Journal of Applied Mathematics*,

*2012*, [696574]. https://doi.org/10.1155/2012/696574

**Analysis of IVPs and BVPs on semi-infinite domains via collocation methods.** / Maleki, Mohammad; Hashim, Ishak; Abbasbandy, Saeid.

Research output: Contribution to journal › Article

*Journal of Applied Mathematics*, vol. 2012, 696574. https://doi.org/10.1155/2012/696574

}

TY - JOUR

T1 - Analysis of IVPs and BVPs on semi-infinite domains via collocation methods

AU - Maleki, Mohammad

AU - Hashim, Ishak

AU - Abbasbandy, Saeid

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84862297300&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862297300&partnerID=8YFLogxK

U2 - 10.1155/2012/696574

DO - 10.1155/2012/696574

M3 - Article

AN - SCOPUS:84862297300

VL - 2012

JO - Journal of Applied Mathematics

JF - Journal of Applied Mathematics

SN - 1110-757X

M1 - 696574

ER -