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math.NA2023
Convolution quadrature for Hadamard fractional calculus and correction methods for the subdiffusion with singular source terms
Baoli Yin, Guoyu Zhang, Yang Liu +1
The convolution quadrature method originally developed for the Riemann-Liouville fractional calculus is extended in this work to the Hadamard fractional calculus by using the expon…
math.NA2023
Sharp error analysis for averaging Crank-Nicolson schemes with corrections for subdiffusion with nonsmooth solutions
Baoli Yin, Yang Liu, Hong Li
Thanks to the singularity of the solution of linear subdiffusion problems, most time-stepping methods on uniform meshes can result in accuracy where denotes the time ste…
math.NA2023
A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation
Guoyu Zhang, Chengming Huang, Anatoly A. Alikhanov +1
The shifted fractional trapezoidal rule (SFTR) with a special shift is adopted to construct a finite difference scheme for the time-fractional Allen-Cahn (tFAC) equation. Some esse…