5 papers
Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using General Multipliers
Chaoyu Quan, Huaijin Wang, Xuping Wang +1
A unified framework is proposed to establish the energy dissipation of implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, based on general multipliers that…
Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier
Chaoyu Quan, Huaijin Wang, Xuping Wang +1
This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constru…
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…
A unified framework on the original energy laws of three effective classes of Runge-Kutta methods for phase field crystal type models
Xuping Wang, Xuan Zhao, Hong-lin Liao
The main theoretical obstacle to establish the original energy dissipation laws of Runge-Kutta methods for phase-field equations is to verify the maximum norm boundedness of the st…
A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model
Hong-lin Liao, Tao Tang, Xuping Wang +1
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of…