An efficient difference scheme based on cubic B-spline Quasi-interpolation  for a time fractional partial integro-differential equation with a weakly singular kernel

Hossein Aminikhah; Mehran Taghipour

doi:10.5269/bspm.62635

Hossein Aminikhah University of Guilan
Mehran Taghipour University of Guilan

Résumé

In this paper, a difference scheme based on cubic B-spline Quasi--interpolation has been derived for the solution of a time fractional partial integro-differential equation with a weakly singular kernel. The fractional derivative of the mentioned equation has been described in the Riemann-Liouville sense. Time fractional derivative is approximated by a scheme of order $O(\tau^{2})$. The spatial second derivative has been approximated using the second derivative of the cubic B-spline Quasi--interpolation. We show that the proposed scheme is uniquely solvable, stable and convergent. It has also been shown that the method is the convergence of order $O(\tau^{\frac{3}{2}}+h^{2})$. Numerical experiments are provided to verify the effectiveness of the proposed method.

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