On conservative, positivity preserving, nonlinear FV scheme on distorted meshes for the multi-term nonlocal Nagumo-type equations
X Yang, Z Zhang - Applied Mathematics Letters, 2024 - Elsevier
The aim of this work is to develop a conservative, positivity-preserving (PP), nonlinear finite
volume (FV) scheme for the multi-term nonlocal Nagumo-type equations on distorted …
volume (FV) scheme for the multi-term nonlocal Nagumo-type equations on distorted …
A generalized SAV approach with relaxation for dissipative systems
Y Zhang, J Shen - Journal of Computational Physics, 2022 - Elsevier
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 …
proposed in [20] are very popular methods to construct efficient and accurate energy stable …
Generalized SAV-exponential integrator schemes for Allen--Cahn type gradient flows
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 …
physical features of the well-known Allen--Cahn equation. While some commonly used first …
Higher-order energy-decreasing exponential time differencing Runge-Kutta methods for gradient flows
In this paper, we develop a general framework for constructing higher-order, unconditionally
energy-decreasing exponential time differencing Runge-Kutta (ETDRK) methods applicable …
energy-decreasing exponential time differencing Runge-Kutta (ETDRK) methods applicable …
Unconditionally maximum bound principle preserving linear schemes for the conservative Allen–Cahn equation with nonlocal constraint
In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …
Stabilized integrating factor Runge--Kutta method and unconditional preservation of maximum bound principle
The maximum bound principle (MBP) is an important property for a large class of semilinear
parabolic equations, in the sense that the time-dependent solution of the equation with …
parabolic equations, in the sense that the time-dependent solution of the equation with …
Energy-decreasing exponential time differencing Runge–Kutta methods for phase-field models
Gradient flow models attract much attention these years. The energy naturally decreases
along the direction of gradient flows. In order to preserve this property, various numerical …
along the direction of gradient flows. In order to preserve this property, various numerical …
Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations
A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP)
in the sense that the time-dependent solution preserves for any time a uniform pointwise …
in the sense that the time-dependent solution preserves for any time a uniform pointwise …
Time-fractional Allen–Cahn equations: analysis and numerical methods
In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
A new class of high-order maximum principle preserving numerical methods is proposed for
solving parabolic equations, with application to the semilinear Allen--Cahn equation. The …
solving parabolic equations, with application to the semilinear Allen--Cahn equation. The …