Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

19-07-2017 | Issue 3/2018

Journal of Scientific Computing 3/2018

Spectral Methods for Substantial Fractional Differential Equations

Journal:
Journal of Scientific Computing > Issue 3/2018
Authors:
Can Huang, Zhimin Zhang, Qingshuo Song
Important notes
The research of Can Huang, is supported by National Natural Science Foundation of China under grant 11401500, 91630204 and the Fundamental Research Funds for the Central Universities under grant 20720150007.
The research of Zhimin Zhang, was supported in part by the National Natural Science Foundation of China under grants 11471031, 91430216, and the US National Science Foundation through grant DMS-1419040.

Abstract

In this paper, a non-polynomial spectral Petrov–Galerkin method and its associated collocation method for substantial fractional differential equations are proposed, analyzed, and tested. We modify a class of generalized Laguerre polynomials to form our trial basis and test basis. After a proper scaling of these bases, our Petrov–Galerkin method results in diagonal and well-conditioned linear systems for certain types of fractional differential equations. In the meantime, we provide superconvergence points of the Petrov–Galerkin approximation for associated fractional derivative and function value of true solution. Additionally, we present explicit fractional differential collocation matrices based upon Laguerre–Gauss–Radau points. It is noteworthy that the proposed methods allow us to adjust a parameter in the basis according to different given data to maximize the convergence rate. All these findings have been proved rigorously in our convergence analysis and confirmed in our numerical experiments.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

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

Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

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




Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 50.000 Bücher
  • über 380 Zeitschriften

aus folgenden Fachgebieten:

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




Testen Sie jetzt 30 Tage kostenlos.

Literature
About this article

Other articles of this Issue 3/2018

Journal of Scientific Computing 3/2018 Go to the issue

Premium Partner

    Image Credits