Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

Abstract

A finite difference/spectral scheme is proposed for the time fractional Ito equation. The mass conservation and stability of the numerical solution are deduced by the energy method in the $L^2$ norm form. To reduce the computation costs, the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations. The effectiveness of the proposed algorithm is verified by the first numerical example. The mass conservation property and stability statement are confirmed by two other numerical examples.

Funding

National Natural Science Foundation of China(11701103); Natural Science Foundation of Guangdong Province(2022A1515012147)