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Shahrokh Esmaeili

Shahrokh Esmaeili

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId: 15834719000
Faculty: Faculty of Science
Address: Department of Mathematics University of Kurdistan
Phone: 08733624133

Research

Title
A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation
Type
JournalPaper
Keywords
fractional derivatives; time-fractional diffusion equations; spectral methods; differentiation matrix; matrix functions
Year
2015
Journal International Journal of Computer Mathematics
DOI
Researchers Shahrokh Esmaeili ، Roberto Garrappa

Abstract

We consider an initial-boundary-value problem for a time-fractional diffusion equation with initial condition $u_0(x)$ and homogeneous Dirichlet boundary conditions in a bounded interval $[0, L]$. We study a semidiscrete approximation scheme based on the pseudo-spectral method on Chebyshev–Gauss–Lobatto nodes. In order to preserve the high accuracy of the spectral approximation we use an approach based on the evaluation of the Mittag-Leffler function on matrix arguments for the integration along the time variable. Some examples are presented and numerical experiments illustrate the effectiveness of the proposed approach.