Open AccessNumerical methods for the time fractional diffusion equation
Author(s) -
Guo Chong,
Fang Zhao
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1324/1/012014
Subject(s) - sinc function , discretization , fractional calculus , mathematics , diffusion equation , collocation method , time derivative , mathematical analysis , numerical analysis , diffusion , collocation (remote sensing) , derivative (finance) , galerkin method , differential equation , ordinary differential equation , finite element method , computer science , physics , economy , machine learning , financial economics , economics , thermodynamics , service (business)
In this paper, a differential analog of the Caputo fractional derivative called the L 2 − 1 σ formula is considered. The time semi-discrete scheme of the time fractional diffusion equation is obtained by using the L 2 − 1 σ formula to discretize the time derivative. The Sinc-Collocation method and the Sinc-Galerkin method are used to discretize the spatial derivatives, and the numerical schemes of the time fractional diffusion equation are constructed. Finally, the validity of the numerical schemes of this paper is verified by numerical example.