An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

N. J. Ford, Maria Luisa Morgado, M. Rebelo

Research output: Contribution to journalArticle

27 Citations (Scopus)
206 Downloads (Pure)

Abstract

In this paper we are concerned with the numerical solution of a diffusion equation in which the time derivative is of non-integer order, i.e., in the interval (0, 1). An implicit numerical method is presented and its unconditional stability and convergence are proved. Two numerical examples are provided to illustrate the obtained theoretical results.

Original languageEnglish
Pages (from-to)289-305
Number of pages17
JournalElectronic transactions on numerical analysis
Volume44
Publication statusPublished - 2015

Keywords

  • Caputo derivative
  • fractional differential equation
  • subdiffusion
  • finite difference method
  • distributed order differential equation
  • FRACTIONAL SUB-DIFFUSION
  • SUBDIFFUSION EQUATION
  • STABILITY
  • SCHEME

Cite this