Numerical solution of fractional diffusion equation by Chebyshev collocation method and residual power series method

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Bayrak M. A., Demir A., Ozbilge E.

Alexandria Engineering Journal, vol.59, pp.4709-4717, 2020 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59
  • Publication Date: 2020
  • Doi Number: 10.1016/j.aej.2020.08.033
  • Journal Name: Alexandria Engineering Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
  • Page Numbers: pp.4709-4717
  • Keywords: Chebyshev collocation method, Fractional diffusion equation, Caputo fractional derivatives, Residual power series method, BAGLEY-TORVIK EQUATION, DIFFERENTIAL-EQUATIONS, APPROXIMATE SOLUTION, ALGORITHM
  • Open Archive Collection: AVESIS Open Access Collection
  • Kocaeli University Affiliated: Yes

Abstract

 Alexandria UniversityIn this paper, we propose an efficient Chebyshev collocation scheme to solve diffusion problem including time fractional diffusion equation considering the fractional derivative in the Liouville-Caputo sense. By making use of shifted Chebyshev polynomial series and their orthogonality properties, the problem is reduced to the system of fractional ordinary differential equations which can be solved by residual power series method (RPSM) with the help of the given scheme and boundary conditions. The numerical examples shows that the method is reliable and effective to construct the numerical solution of fractional diffusion equation.