Numerical solution for solving fractional parabolic partial differential equations

In this paper, a reliable numerical scheme is developed and reviewed in order to obtain an approximate solution of time-fractional parabolic partial differential equations. The introduced scheme is based on Legendre tau spectral approximation and the time-fractional derivative is employed in the Caputo sense. The L۲ convergence analysis of the numerical method is analyzed. Numerical results for different examples are examined to verify the accuracy of the spectral method and justification the theoretical analysis and to compare with other existing methods in the literatures.

Keywords:

Time fractional parabolic partial differential equations , Caputo derivative , Shifted Legendre Tau method