Computational methods for delay parabolic and time-fractional partial differential equations

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44 Citations (Scopus)

Abstract

This article is concerned with ?-methods for delay parabolic partial differential equations. The methodology is extended to time-fractional-order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay-independent asymptotic stability and the solution continuously depends on the time-fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method.

Original languageEnglish
Pages (from-to)1556-1571
Number of pages16
JournalNumerical Methods for Partial Differential Equations
Volume26
Issue number6
DOIs
Publication statusPublished - Nov 2010

Keywords

  • ?-methods
  • Diffusion equations
  • Discretization
  • Fractional derivative order
  • Runke-Kutta
  • Stability regions
  • Stiffness
  • Time-lag

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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