Chebyshev spectral approximation for diffusion equations with distributed order in time

Maria Luísa Morgado, Magda Rebelo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.

Original languageEnglish
Title of host publicationDifferential and Difference Equations with Applications - ICDDEA, Selected Contributions
PublisherSpringer New York LLC
Pages255-263
Number of pages9
Volume164
ISBN (Print)9783319328553
DOIs
Publication statusPublished - 2016
EventInternational Conference on Differential and Difference Equations with Applications, ICDDEA 2015 - Amadora, Portugal
Duration: 18 May 201522 May 2015

Conference

ConferenceInternational Conference on Differential and Difference Equations with Applications, ICDDEA 2015
CountryPortugal
CityAmadora
Period18/05/1522/05/15

Keywords

  • Caputo derivative
  • Chebyshev polynomials
  • Diffusion equation
  • Distributed order equation
  • Fractional differential equation

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