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

Zahari Zlatev, I. Faragó, Ágnes Havasi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages54-66
Number of pages13
Volume5910 LNCS
DOIs
Publication statusPublished - 2010
Event7th International Conference on Large-Scale Scientific Computations, LSSC 2009 - Sozopol, Bulgaria
Duration: Jun 4 2009Jun 8 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5910 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Conference on Large-Scale Scientific Computations, LSSC 2009
CountryBulgaria
CitySozopol
Period6/4/096/8/09

Fingerprint

Richardson Extrapolation
Convergence of numerical methods
System of Ordinary Differential Equations
Extrapolation
Ordinary differential equations
Numerical methods
Numerical Methods
Grid
Approximation
Relationships

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Zlatev, Z., Faragó, I., & Havasi, Á. (2010). On some stability properties of the Richardson Extrapolation applied together with the θ-method. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5910 LNCS 2010. p. 54-66 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5910 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zlatev, Z, Faragó, I & Havasi, Á 2010, On some stability properties of the Richardson Extrapolation applied together with the θ-method. in 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
Zlatev Z, Faragó I, Havasi Á. On some stability properties of the Richardson Extrapolation applied together with the θ-method. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5910 LNCS. 2010. p. 54-66. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-12535-5_5
Zlatev, Zahari ; Faragó, I. ; Havasi, Ágnes. / On some stability properties of the Richardson Extrapolation applied together with the θ-method. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5910 LNCS 2010. pp. 54-66 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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