10.1007/s40096-021-00447-9

Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method

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  • Sh. Taherkhani1,
  • I. Najafi Khalilsaraye*1,
  • B. Ghayebi1,
  1. Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IR

Published in Issue 2021-11-21

How to Cite

Taherkhani, S., Khalilsaraye, I. N., & Ghayebi, B. (2021). Numerical solution of the diffusion problem of distributed order based on the Sinc-collocation method. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00447-9
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Abstract

Abstract A numerical method for the diffusion problem with the fractional derivative of distributed order arising in modeling real life phenomena is investigated. The approximation is based on the Sinc-collocation method. We proposed the Sinc-collocation method in both spatial and temporal discretizations of the problem. The fractional derivatives in this article are of the Caputo type. Also, we proved the convergence of the introduced method and an error estimate for it. We have shown the efficiency of the introduced method with the help of several examples. The obtained numerical results confirm the presented convergence analysis.

Keywords

  • Fractional differential equation,
  • Distributed order differential equation,
  • Caputo derivative,
  • Sinc basis,
  • Collocation method

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