A new fast parallel difference scheme for nonlinear time fractional reaction-diffusion equation on graded meshes

Shucai Wang; Xin Gao; Lifei Wu

doi:10.1117/12.3052926

3 January 2025 A new fast parallel difference scheme for nonlinear time fractional reaction-diffusion equation on graded meshes

Shucai Wang, Xin Gao, Lifei Wu

Author Affiliations +

Proceedings Volume 13442, Fifth International Conference on Signal Processing and Computer Science (SPCS 2024); 134421U (2025) https://doi.org/10.1117/12.3052926
Event: Fifth International Conference on Signal Processing and Computer Science (SPCS 2024), 2024, Kaifeng, China

Abstract

The nonlinear time fractional reaction-diffusion (TFRD) equation is an important class of fractional parabolic equations, and the study of its numerical methods has important scientific significance and application value. This paper proposes a new fast alternating segmented Crank-Nicolson (FASC-N) parallel difference scheme on graded meshes for solving the singular problem of nonlinear TFRD equation. To construct the FASC-N scheme, the time term is approximated by using fast L1 approximation of the time fractional derivative on graded meshes. Based on the alternating technique, the space term is discreteted by Crank-Nicolson (C-N) difference scheme and four kinds of Saulyev asymmetric difference scheme. It is proved that FASC-N scheme is unconditionally stable and has good convergence. Numerical experiment shows that FASC-N scheme has a feature that the calculation accuracy is improved with the decrease of grid ratio. The scheme has good parallel property, and the calculation efficiency is obviously better than the classical serial scheme, which is an efficient method to solve nonlinear TFRD equation.

(2025) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Shucai Wang, Xin Gao, and Lifei Wu "A new fast parallel difference scheme for nonlinear time fractional reaction-diffusion equation on graded meshes", Proc. SPIE 13442, Fifth International Conference on Signal Processing and Computer Science (SPCS 2024), 134421U (3 January 2025); https://doi.org/10.1117/12.3052926

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