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A fast compact difference scheme on graded meshes for solving the time . . . A fast compact difference (FCD) scheme on graded meshes is used to address the time-fractional nonlinear KdV equation with an initial singularity The temporal discretization employs the fast L1 algorithm, while a fourth-order compact scheme is utilized for spatial discretization
journal. global-sci. org Combined with the fast $L1$ time-stepping method on graded temporal meshes, we develop and analyze a fourth-order compact block-centered finite difference (BCFD) method
Error Analysis of a Finite Difference Method on Graded Meshes for a . . . A new analysis of a standard finite difference method for the problem is given, taking into account this initial singularity This analysis encompasses both uniform meshes and meshes that are graded in time, and includes new stability and consistency bounds
L1-robust analysis of a fourth-order block-centered finite difference . . . For the two-dimensional time-fractional reaction-diffusion equations with variably diffusion coefficient and general reaction (positive or negative), we construct a fourth-order BCFD method on staggered uniform spatial meshes combined with L1 discretization on graded temporal mesh