### Abstract

Consider the system of ordinary differential equation (ODEs) dy/dt∈=∈f(t,y) where (a) t∈ ∈[a,b] with b∈>∈a , (b) y is a vector containing s components and (c) y(a) is given. The θ-method is applied to solve approximately the system of ODEs on a set of prescribed grid-points. If N is the number of time-steps that are to be carried out, then this numerical method can be defined by using the following set of relationships y _{n} ∈=∈y _{n∈-∈1}∈+∈h (1∈-∈θ) f(t _{n∈-∈1}, y _{n∈-∈1}) , θ∈ ∈[0.5, 1.0] , n∈=∈1, 2, ..., N , h∈=∈(b∈-∈a) / N , t _{n} ∈=∈t _{n∈-∈1}∈+∈h∈=∈t _{0}∈+∈ n h , t _{0}=∈a , t _{N} =∈b . As a rule, the accuracy of the approximations { y _{n}

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 54-66 |

Number of pages | 13 |

Volume | 5910 LNCS |

DOIs | |

Publication status | Published - 2010 |

Event | 7th International Conference on Large-Scale Scientific Computations, LSSC 2009 - Sozopol, Bulgaria Duration: Jun 4 2009 → Jun 8 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5910 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 7th International Conference on Large-Scale Scientific Computations, LSSC 2009 |
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Country | Bulgaria |

City | Sozopol |

Period | 6/4/09 → 6/8/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5910 LNCS, pp. 54-66). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5910 LNCS). https://doi.org/10.1007/978-3-642-12535-5_5

**On some stability properties of the Richardson Extrapolation applied together with the θ-method.** / Zlatev, Zahari; Faragó, I.; Havasi, Ágnes.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5910 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5910 LNCS, pp. 54-66, 7th International Conference on Large-Scale Scientific Computations, LSSC 2009, Sozopol, Bulgaria, 6/4/09. https://doi.org/10.1007/978-3-642-12535-5_5

}

TY - GEN

T1 - On some stability properties of the Richardson Extrapolation applied together with the θ-method

AU - Zlatev, Zahari

AU - Faragó, I.

AU - Havasi, Ágnes

PY - 2010

Y1 - 2010

N2 - Consider the system of ordinary differential equation (ODEs) dy/dt∈=∈f(t,y) where (a) t∈ ∈[a,b] with b∈>∈a , (b) y is a vector containing s components and (c) y(a) is given. The θ-method is applied to solve approximately the system of ODEs on a set of prescribed grid-points. If N is the number of time-steps that are to be carried out, then this numerical method can be defined by using the following set of relationships y n ∈=∈y n∈-∈1∈+∈h (1∈-∈θ) f(t n∈-∈1, y n∈-∈1) , θ∈ ∈[0.5, 1.0] , n∈=∈1, 2, ..., N , h∈=∈(b∈-∈a) / N , t n ∈=∈t n∈-∈1∈+∈h∈=∈t 0∈+∈ n h , t 0=∈a , t N =∈b . As a rule, the accuracy of the approximations { y n

AB - Consider the system of ordinary differential equation (ODEs) dy/dt∈=∈f(t,y) where (a) t∈ ∈[a,b] with b∈>∈a , (b) y is a vector containing s components and (c) y(a) is given. The θ-method is applied to solve approximately the system of ODEs on a set of prescribed grid-points. If N is the number of time-steps that are to be carried out, then this numerical method can be defined by using the following set of relationships y n ∈=∈y n∈-∈1∈+∈h (1∈-∈θ) f(t n∈-∈1, y n∈-∈1) , θ∈ ∈[0.5, 1.0] , n∈=∈1, 2, ..., N , h∈=∈(b∈-∈a) / N , t n ∈=∈t n∈-∈1∈+∈h∈=∈t 0∈+∈ n h , t 0=∈a , t N =∈b . As a rule, the accuracy of the approximations { y n

UR - http://www.scopus.com/inward/record.url?scp=77953767518&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953767518&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-12535-5_5

DO - 10.1007/978-3-642-12535-5_5

M3 - Conference contribution

AN - SCOPUS:77953767518

SN - 3642125344

SN - 9783642125348

VL - 5910 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 54

EP - 66

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -