The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

The scalar auxiliary variable (SAV) approach [31] and its generalized version GSAV
proposed in [20] are very popular methods to construct efficient and accurate energy stable …

The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …

In this paper, we develop a general framework for constructing higher-order, unconditionally
energy-decreasing exponential time differencing Runge-Kutta (ETDRK) methods applicable …

It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of
the problems and the requirement of highly stable and energy-preserving schemes. The …

Spatial discretizations of time-dependent partial differential equations usually result in a
large system of semi-linear and stiff ordinary differential equations. Taking the structures into …

It is well-known that the Allen–Cahn equation not only satisfies the energy dissipation law
but also possesses the maximum bound principle (MBP) in the sense that the absolute value …

We construct a new class of efficient implicit–explicit (IMEX) BDF k schemes combined with
a scalar auxiliary variable (SAV) approach for general dissipative systems. We show that …

We present a paradigm for develo** arbitrarily high order, linear, unconditionally energy
stable numerical algorithms for general gradient flow models. We apply the energy …

We construct new first-and second-order pressure correctionschemes using the scalar
auxiliary variable approach for the Navier-Stokes equations. These schemes are linear …