A fractional spline collocation-Galerkin method for the time-fractional diffusion equation
This work provides a numerical method for solving time-fractional diffusion equations, which is incremental in the context of existing fractional PDE solvers.
The paper proposes a collocation-Galerkin method using fractional splines to solve time-fractional diffusion equations, achieving accurate and efficient numerical solutions as demonstrated by several tests.
The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.