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math.NA2026
Long-time stability of implicit-explicit Runge-Kutta methods for two-dimensional incompressible flows
Hong-lin Liao, Xiaoming Wang, Xuping Wang +1
High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dyn…
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
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…