BDF$6$ SAV schemes for time-fractional Allen-Cahn dissipative systems

TL;DR

This paper develops and analyzes BDF6 SAV schemes for time-fractional Allen-Cahn dissipative systems, providing the first such schemes and their rigorous error analysis, supported by numerical experiments.

Contribution

It introduces the first BDF6 SAV schemes for time-fractional dissipative systems and provides a comprehensive error analysis, filling a gap in existing research.

Findings

Successful construction of BDF6 SAV schemes for time-fractional systems

Rigorous error analysis confirming scheme stability and accuracy

Numerical experiments demonstrating effectiveness of the methods

Abstract

Recently, the error analysis of BDF$k$ $(1\leqslant k\leqslant5)$ SAV (scalar auxiliary variable) schemes are given in \cite{Huangg:20} for the classical Allen-Cahn equation. However, it remains unavailable for BDF$6$ SAV schemes. In this paper, we construct and analyze BDF$6$ SAV schemes for the time-fractional dissipative systems. We carry out a rigorous error analysis for the time-fractional Allen-Cahn equation, which also fills up a gap for the classical case. Finally, numerical experiment is shown to illustrate the effectiveness of the presented methods. As far as we know, this is the first SAV schemes for the time-fractional dissipative systems.