Third-order accurate, large time-step** and maximum-principle-preserving schemes for the Allen-Cahn equation

H Zhang, X Qian, S Song - Numerical Algorithms, 2024 - Springer
We present and evaluate several explicit, large time-step** algorithms for the Allen-Cahn
equation. Our approach incorporates a stabilization technique and uses Taylor series …

Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions

H Zhang, X Qian, J ** explicit, high-order accurate, and stable algorithms for nonlinear differential
equations remains an exceedingly difficult task. In this work, a systematic approach is …

Large time-step**, delay-free, and invariant-set-preserving integrators for the viscous Cahn–Hilliard–Oono equation

H Zhang, L Liu, X Qian, S Song - Journal of Computational Physics, 2024 - Elsevier
Stabilization techniques are frequently used to construct efficient and stable schemes for stiff
and nonlinear systems. However, the introduced errors may lead to severe delay effects …

High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation

Z Gao, H Zhang, X Qian, S Song - Applied Numerical Mathematics, 2023 - Elsevier
We utilize the second-order quadrature-based finite difference method and the high-order
parametric integrating factor Runge-Kutta (pIFRK) integrators to construct efficient and …

Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

H Zhang, L Liu, X Qian, S Song - ESAIM: Mathematical Modelling …, 2024 - esaim-m2an.org
Although the stabilization technique is favorable in designing unconditionally energy stable
or maximum-principle-preserving schemes for gradient flow systems, the induced time delay …

Singly TASE operators for the numerical solution of stiff differential equations by explicit Runge–Kutta schemes

M Calvo, L Fu, JI Montijano, L Liu, H Zhang, X Qian, S Song - Communications in Nonlinear Science …, 2024 - Elsevier
In this paper, we construct a class of temporal up-to-fourth-order integrators that preserve
strong stability of conservation laws for relatively large time steps. The new methods …