Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method

Maria Lu�sa Morgado, Magda Rebelo, Luis L. Ferrás, Neville J. Ford

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In this work we present a new numerical method for the solution of the distributed order time-fractional diffusion equation. The method is based on the approximation of the solution by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points. An error analysis is provided and a comparison with other methods used in the solution of this type of equation is also performed.

Original languageEnglish
Pages (from-to)108-123
Number of pages16
JournalApplied Numerical Mathematics
Volume114
DOIs
Publication statusPublished - Apr 2017

Keywords

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

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