Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2021

22.11.2020 | Original Research

EBDF-type methods based on the linear barycentric rational interpolants for stiff IVPs

verfasst von: Zahra Esmaeelzadeh, Ali Abdi, Gholamreza Hojjati

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Linear barycentric rational interpolants, instead of customary polynomial interpolants, have been recently used to design the efficient numerical integrators for ODEs. In this way, the BDF-type methods based on these interpolants have been introduced as a general class of the methods in this type with better accuracy and stability properties. In this paper, we introduce an extension of them equipped to super-future point technique. The order of convergence and stability of the proposed methods are discussed and confirmed by some given numerical experiments.
Vorheriger Artikel Further results on the signed Italian domination
Nächster Artikel A novel numerical scheme for a time fractional Black–Scholes equation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Abdi, A., Berrut, J.P., Hosseini, S.A.: Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations. (submitted)
2.
Abdi, A., Berrut, J.P., Hosseini, S.A.: The linear barycentric rational method for a class of delay Volterra integro-differential equations. J. Sci. Comput. 75, 1757–1775 (2018)MathSciNetMATHCrossRef
3.
Abdi, A., Hojjati, G.: Barycentric rational interpolants based second derivative backward differentiation formulae for ODEs. Numer. Algorithms 85, 867–886 (2020)
4.
Abdi, A., Hosseini, S.A.: The barycentric rational difference-quadrature scheme for systems of Volterra integro-differential equations. SIAM J. Sci. Comput. 40, A1936–A1960 (2018)MathSciNetMATHCrossRef
5.
Abdi, A., Hosseini, S.A., Podhaisky, H.: Adaptive linear barycentric rational finite differences method for stiff ODEs. J. Comput. Appl. Math. 357, 204–214 (2019)MathSciNetMATHCrossRef
6.
Abdi, A., Hosseini, S.A., Podhaisky, H.: Numerical methods based on the Floater–Hormann interpolants for stiff VIEs. Numer. Algorithm (to appear)
7.
Atkinson, K.E.: An Introduction to Numerical Analysis. Wiley, New York (1989)MATH
8.
Berrut, J.P.: Rational functions for guaranteed and experimentally well-conditioned global interpolation. Comput. Math. Appl. 15, 1–16 (1988)MathSciNetMATHCrossRef
9.
Berrut, J.P., Floater, M.S., Klein, G.: Convergence rates of derivatives of a family of barycentric rational interpolants. Appl. Numer. Math. 61, 989–1000 (2011)MathSciNetMATHCrossRef
10.
Berrut, J.P., Hosseini, S.A., Klein, G.: The linear barycentric rational quadrature method for Volterra integral equations. SIAM J. Sci. Comput. 36, A105–A123 (2014)MathSciNetMATHCrossRef
11.
Berrut, J.P., Trefethen, L.N.: Barycentric lagrange interpolation. SIAM J. Numer. Anal. 46, 501–517 (2004)MathSciNetMATH
12.
Butcher, J.C.: A modified multistep method for the numerical integration of ordinary differential equations. J. ACM 12, 124–135 (1965)MathSciNetMATHCrossRef
13.
Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester (2016)MATHCrossRef
14.
Cash, J.R.: On the integration of stiff systems of ODEs using extended backward differentiation formulae. Numer. Math. 34, 235–246 (1980)MathSciNetMATHCrossRef
15.
Cash, J.R.: Second derivative extended backward differentiation formulas for the numerical integration of stiff systems. SIAM J. Numer. Anal. 18, 21–36 (1981)MathSciNetMATHCrossRef
16.
Cash, J.R.: The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae. Comput. Math. Appl. 9, 645–657 (1983)MathSciNetMATHCrossRef
17.
18.
19.
Dahlquist, G.: Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand. 4, 33–53 (1956)MathSciNetMATHCrossRef
20.
Enright, W.H.: Second derivative multistep methods for stiff ordinary differential equations. SIAM J. Numer. Anal. 11, 321–331 (1974)MathSciNetMATHCrossRef
21.
Floater, M.S., Hormann, K.: Barycentric rational interpolation with no poles and high rates of approximation. Numer. Math. 107, 315–331 (2007)MathSciNetMATHCrossRef
22.
23.
Gear, C.W.: Hybrid methods for initial value problems in ordinary differential equations. SIAM J. Numer. Anal. 2, 69–86 (1965)MathSciNetMATH
24.
25.
Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, Berlin (2010)MATH
26.
Hojjati, G., Rahimi Ardabili, M.Y., Hosseini, S.M.: A-EBDF: an adaptive method for numerical solution of stiff systems of ODEs. Math. Comput. Simul. 66, 33–41 (2004)MathSciNetMATHCrossRef
27.
Hojjati, G., Rahimi Ardabili, M.Y., Hosseini, S.M.: New second derivative multistep methods for stiff systems. Appl. Math. Model. 30, 466–476 (2006)MATHCrossRef
28.
Hosseini, S.A., Abdi, A.: On the numerical stability of the linear barycentric rational quadrature method for Volterra integral equations. Appl. Numer. Math. 100, 1–13 (2016)MathSciNetMATHCrossRef
29.
Klein, G.: Applications of Linear Barycentric Rational Interpolation. PhD thesis, University of Fribourg (2012)
30.
Klein, G., Berrut, J.P.: Linear rational finite differences from derivatives of barycentric rational interpolants. SIAM J. Numer. Anal. 50, 643–656 (2012)MathSciNetMATHCrossRef
31.
Metadaten
Titel
EBDF-type methods based on the linear barycentric rational interpolants for stiff IVPs
verfasst von
Zahra Esmaeelzadeh
Ali Abdi
Gholamreza Hojjati
Publikationsdatum
22.11.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01464-y

Weitere Artikel der Ausgabe 1-2/2021

Journal of Applied Mathematics and Computing 1-2/2021 Zur Ausgabe

Original Research

Solving two generalized nonlinear matrix equations

Original Research

A novel approach for the solution of BVPs via Green’s function and fixed point iterative method

Original Research

Deciphering role of inter and intracity human dispersal on epidemic spread via coupled reaction-diffusion models

Original Research

A limited memory q-BFGS algorithm for unconstrained optimization problems

Original Research

Stationary distribution and extinction of a stochastic model of syphilis transmission in an MSM population with telegraph noises

Original Research

On the global asymptotic stability of a system of difference equations with quadratic terms

Premium Partner

    Bildnachweise