Abstract
A Crank-Nicolson-type difference scheme is presented for the spatial variable coefficient subdiffusion equation with Riemann-Liouville fractional derivative. The truncation errors in temporal and spatial directions are analyzed rigorously. At each time level, it results in a linear system in which the coefficient matrix is tridiagonal and strictly diagonally dominant, so it can be solved by the Thomas algorithm. The unconditional stability and convergence of the scheme are proved in the discrete L_{2} norm by the energy method. The convergence order is min {2-frac{alpha}{2}, 1+alpha } in the temporal direction and two in the spatial one. Finally, numerical examples are presented to verify the efficiency of our method.
Highlights
In recent years, fractional differential equations have captured great attention of research in different domains
Employing fractional derivatives to describe the procedure of anomalous diffusion, we get the time fractional subdiffusion equation [, ]:
Gao and Sun [ ] applied the L formula to approximate the Caputo time-fractional derivative and developed a compact finite difference scheme to promote the spatial accuracy for the fractional subdiffusion equation
Summary
Fractional differential equations have captured great attention of research in different domains. In the regard of numerical work for time-fractional diffusion equations, Langlands and Henry [ ] obtained an implicit numerical method for the homogeneous problem and discussed the accuracy and stability of their scheme. Sun and Wu [ ] first derived a fully discrete difference scheme employing the L approximation, where the truncation error was proved to be of order – α in temporal accuracy.
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