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20242026
most citedMaximum bound principle and original energy dissipation of arbitrarily high-order rescaled exponential time differencing Runge-Kutta schemes for Allen--Cahn equations

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math.NA2024

A note on the stability of two families of two-step schemes

Xiaoming Wang, Yinqian Yu

We investigate the stability of two families of three-level two-step schemes that extend the classical second order BDF (BDF2) and second order Adams-Moulton (AM2) schemes. For a f…

math.NA2024★ 1 cited

Maximum bound principle and original energy dissipation of arbitrarily high-order rescaled exponential time differencing Runge-Kutta schemes for Allen--Cahn equations

Chaoyu Quan, Xiaoming Wang, Pinzhong Zheng +1

The energy dissipation law and the maximum bound principle are two critical physical properties of the Allen--Cahn equations. While many existing time-stepping methods are known to…