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Third-order accurate, large time-step** and maximum-principle-preserving schemes for the Allen-Cahn equation
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 …
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 …
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
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 …
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
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 …
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
Although the stabilization technique is favorable in designing unconditionally energy stable
or maximum-principle-preserving schemes for gradient flow systems, the induced time delay …
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 …
strong stability of conservation laws for relatively large time steps. The new methods …