GM

Note

The MATLAB codes for the research paper: Can Wang, Weihua Deng, and Xiangong Tang. "A sharp $\alpha$-robust $L1$ scheme on graded meshes for two-dimensional time tempered fractional Fokker-Planck equation." Int. J. Numer. Anal. Mod. 20, 739-771 (2023).

Warning

The publication information mentioned here such as the doi, may differ from the officially published version. Once this happens, we will correct it immediately.

Introduction

The paper mentioned above mainly discusses the numerical solution for the two-dimensional time fractional Fokker-Planck equation (see below) with the temperd fractional derivative of order $\alpha$, where a modified $L1$ scheme on graded meshes is employed to temporal discretization, and in the spatial direction, the five-point difference scheme is used.

$$\partial_t^{\alpha, \sigma}u(x,y,t)=\Delta u(x,y,t)+f(x,y,t),\qquad (x,y,t)\in \Omega\times (0, T],$$

with homogeneous Dirichlet boundary condition and the initial values being $u_0(x,y)$.

Codes

.
├── README.md
├── graded_solver.m
├── l1.m
├── l1exp.m
└── test.m

Citation

@article{wang2023tempered
title = {A sharp $\alpha$-robust $L1$ scheme on graded meshes for two-dimensional time tempered fractional Fokker-Planck equation},
author = {Wang, Can and Deng, Weihua and Tang, Xiangong},
journal = {Int. J. Numer. Anal. Mod.},
volume = {20},
number = {6},
pages = {739--771},
year = {2023}
}