Compact finite difference method for the fractional diffusion equation

By Mingrong Cui. Journal of Computational Physics, 2009

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Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “Second, one may develop fast high-order algorithms for solving fractional PDEs which contains fractional derivatives in both time and space when the current scheme is combined with other existing schemes [10, 11, 12, 28].”
A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations (2015, methodology): “In [32,33], Cui presented high-order compact finite difference methods to solve the fractional diffusion and time fractional diffusion equation.”
The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “Cui [10] derived a compact implicit finite difference method for (1.”
A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions (2018, methodology): “In [18], Cui presented highorder compact finite difference methods to solve the fractional diffusion and time fractional diffusion equation.”
Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation (2013, unknown): “2 Consider the following example ([35, 36]).”