Numerical approximation of distributed order reaction-diffusion equations

Maria Luisa Morgado, M. Rebelo

Research output: Contribution to journalArticle

Abstract

In this paper an implicit scheme for the numerical approximation of the distributed order time-fractional reaction-diffusion equation with a nonlinear source term is presented. The stability and the convergence order of the numerical scheme are analysed and illustrated through some numerical examples. 

Original languageEnglish
Pages (from-to)216-227
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume275
DOIs
Publication statusPublished - Feb 2015

Keywords

  • Fractional differential equation
  • Caputo derivative
  • Diffusion equation
  • Implicit finite difference method
  • Distributed order equation
  • TIME-FRACTIONAL DIFFUSION
  • FINITE-DIFFERENCE METHODS
  • SUB-DIFFUSION
  • SUBDIFFUSION EQUATION
  • TERM
  • STABILITY
  • SCHEME

Cite this

@article{530d264ddfcc4cbb833b1f0c9cd099d2,
title = "Numerical approximation of distributed order reaction-diffusion equations",
abstract = "In this paper an implicit scheme for the numerical approximation of the distributed order time-fractional reaction-diffusion equation with a nonlinear source term is presented. The stability and the convergence order of the numerical scheme are analysed and illustrated through some numerical examples. ",
keywords = "Fractional differential equation, Caputo derivative, Diffusion equation, Implicit finite difference method, Distributed order equation, TIME-FRACTIONAL DIFFUSION, FINITE-DIFFERENCE METHODS, SUB-DIFFUSION, SUBDIFFUSION EQUATION, TERM, STABILITY, SCHEME",
author = "Morgado, {Maria Luisa} and M. Rebelo",
note = "The authors acknowledge financial support from Portuguese Foundation for Science and Technology (FCT) within projects PEst-OE/MAT/UI4080/2014 and PEst-OE/MAT/UI0822/2014.",
year = "2015",
month = "2",
doi = "10.1016/j.cam.2014.07.029",
language = "English",
volume = "275",
pages = "216--227",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier Science B.V., Inc",

}

Numerical approximation of distributed order reaction-diffusion equations. / Morgado, Maria Luisa ; Rebelo, M.

In: Journal of Computational and Applied Mathematics, Vol. 275, 02.2015, p. 216-227.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical approximation of distributed order reaction-diffusion equations

AU - Morgado, Maria Luisa

AU - Rebelo, M.

N1 - The authors acknowledge financial support from Portuguese Foundation for Science and Technology (FCT) within projects PEst-OE/MAT/UI4080/2014 and PEst-OE/MAT/UI0822/2014.

PY - 2015/2

Y1 - 2015/2

N2 - In this paper an implicit scheme for the numerical approximation of the distributed order time-fractional reaction-diffusion equation with a nonlinear source term is presented. The stability and the convergence order of the numerical scheme are analysed and illustrated through some numerical examples. 

AB - In this paper an implicit scheme for the numerical approximation of the distributed order time-fractional reaction-diffusion equation with a nonlinear source term is presented. The stability and the convergence order of the numerical scheme are analysed and illustrated through some numerical examples. 

KW - Fractional differential equation

KW - Caputo derivative

KW - Diffusion equation

KW - Implicit finite difference method

KW - Distributed order equation

KW - TIME-FRACTIONAL DIFFUSION

KW - FINITE-DIFFERENCE METHODS

KW - SUB-DIFFUSION

KW - SUBDIFFUSION EQUATION

KW - TERM

KW - STABILITY

KW - SCHEME

U2 - 10.1016/j.cam.2014.07.029

DO - 10.1016/j.cam.2014.07.029

M3 - Article

VL - 275

SP - 216

EP - 227

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -