Abstract
In this paper, we have considered the fractional diffusion and fractional diffusion-wave equations in which the time derivative is a fractional derivative in the Caputo form and have obtained their numerical solutions by collocation method using cubic B-spline base functions. In the solution process, for the fractional diffusion equation $L1$ discretizaton formula of the fractional derivative is applied, and for the fractional diffusion-wave equation $L2$ discretizaton formula of the fractional derivative is applied. Accuracy of the proposed method is discussed by computing the error norms $L_{2}$ and $L_{\infty}$ . A stability analysis of the approximation obtained by the scheme shows that the method is unconditionally stable.
Citation
A. Esen. O. Tasbozan. Y. Ucar. N.M. Yagmurlu. "A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations." Tbilisi Math. J. 8 (2) 181 - 193, December 2015. https://doi.org/10.1515/tmj-2015-0020
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