In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L2 and L∞ are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.
Esen, A., Ucar, Y., Yagmurlu, N., & Tasbozan, O. (2013). A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations. Mathematical Modelling and Analysis, 18(2), 260-273. https://doi.org/10.3846/13926292.2013.783884
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