# Optimal stability polynomials for numerical integration of initial value problems

- Handle URI:
- http://hdl.handle.net/10754/333599
- Title:
- Optimal stability polynomials for numerical integration of initial value problems
- Authors:
- Abstract:
- We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
- KAUST Department:
- Citation:
- Optimal stability polynomials for numerical integration of initial value problems 2012, 7 (2):247 Communications in Applied Mathematics and Computational Science
- Publisher:
- Journal:
- Issue Date:
- 8-Jan-2013
- DOI:
- 10.2140/camcos.2012.7.247
- ARXIV:
- arXiv:1201.3035
- Type:
- Article
- ISSN:
- 2157-5452; 1559-3940
- Additional Links:
- http://msp.org/camcos/2012/7-2/p04.xhtml; http://github.com/ketch/RK-opt; http://arxiv.org/abs/1201.3035

- Appears in Collections:
- Articles; Numerical Mathematics Group; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

# Full metadata record

DC Field | Value | Language |
---|---|---|

dc.contributor.author | Ketcheson, David I. | en |

dc.contributor.author | Ahmadia, Aron | en |

dc.date.accessioned | 2014-11-03T16:17:27Z | - |

dc.date.available | 2014-11-03T16:17:27Z | - |

dc.date.issued | 2013-01-08 | en |

dc.identifier.citation | Optimal stability polynomials for numerical integration of initial value problems 2012, 7 (2):247 Communications in Applied Mathematics and Computational Science | en |

dc.identifier.issn | 2157-5452 | en |

dc.identifier.issn | 1559-3940 | en |

dc.identifier.doi | 10.2140/camcos.2012.7.247 | en |

dc.identifier.uri | http://hdl.handle.net/10754/333599 | en |

dc.description.abstract | We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied. | en |

dc.language.iso | en | en |

dc.publisher | Mathematical Sciences Publishers | en |

dc.relation.url | http://msp.org/camcos/2012/7-2/p04.xhtml | en |

dc.relation.url | http://github.com/ketch/RK-opt | en |

dc.relation.url | http://arxiv.org/abs/1201.3035 | en |

dc.rights | Archived with thanks to Communications in Applied Mathematics and Computational Science | en |

dc.subject | absolute stability | en |

dc.subject | initial value problems | en |

dc.subject | Runge–Kutta methods | en |

dc.title | Optimal stability polynomials for numerical integration of initial value problems | en |

dc.type | Article | en |

dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | en |

dc.contributor.department | Numerical Mathematics Group | en |

dc.identifier.journal | Communications in Applied Mathematics and Computational Science | en |

dc.eprint.version | Publisher's Version/PDF | en |

dc.contributor.affiliation | King Abdullah University of Science and Technology (KAUST) | en |

dc.identifier.arxivid | arXiv:1201.3035 | en |

kaust.author | Ketcheson, David I. | en |

kaust.author | Ahmadia, Aron | en |

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