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

doi:10.1007/s42967-022-00223-z

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4): 1591-1600.doi: 10.1007/s42967-022-00223-z

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

Dakang Cen^1,2, Zhibo Wang¹, Seakweng Vong²

1 School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;
2 Department of Mathematics, University of Macau, Macau, China

Received:2022-07-20 Revised:2022-10-18 Published:2023-12-16
Contact: Zhibo Wang,E-mail:wzbmath@gdut.edu.cn;Dakang Cen,E-mail:cendakang@163.com;Seakweng Vong,E-mail:swvong@um.edu.mo E-mail:wzbmath@gdut.edu.cn;cendakang@163.com;swvong@um.edu.mo
Supported by:
This research was partly supported by the National Natural Science Foundation of China (No. 11701103), the Young Top-notch Talent Program of Guangdong Province of China (No. 2017GC010379), the Natural Science Foundation of Guangdong Province of China (No. 2022A1515012147), the Project of Science and Technology of Guangzhou of China (No. 202102020704), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University of China (2021023), the Science and Technology Development Fund, Macau SAR (File No. 0005/2019/A), and the University of Macau of China (File Nos. MYRG2020-00035-FST, MYRG2018-00047-FST).

Abstract

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 L² 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.

Key words: Time fractional Ito equation, Finite difference method, Spectral method, Stability

CLC Number:

Dakang Cen, Zhibo Wang, Seakweng Vong. Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic[J]. Communications on Applied Mathematics and Computation, 2023, 5(4): 1591-1600.

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References

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

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