Two novel energy dissipative difference schemes for the strongly coupled nonlinear space fractional wave equations with damping

Xie, Jianqiang; Dong, Liang; Zhang, Zhiyue

doi:10.1016/j.apnum.2020.06.002

Cited by 6 publications

(3 citation statements)

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“…In this example, we simulate the phase separation dynamics that is called spinodal decomposition by using the EL-SARK (3,5) scheme (29), and the cases using other schemes are similar to this. Consider the mass-conservative AC equation in Equation (1) as subject to the initial condition [13] u 0 (x, y) = 0.5…”

Section: Spinodal Decomposition In 2dmentioning

confidence: 99%

“…All RK methods preserve arbitrary linear invariants [41]. Inspired by the idea of invariant energy quadratization (IEQ) approach and scalar auxiliary variable (SAV) approach [29,42,43], in this work, we propose three high-order accurate and unconditionally energy-stable methods for Equation (1). One is based on an energy linearization Runge-Kutta (EL-RK) method, in which an energy linearization strategy is adopted to compute the energy, that is, the energy related to the nonlinear terms is obtained in an explicit way by computing an equivalent auxiliary variable with some specific class of RK schemes.…”

Section: Introductionmentioning

confidence: 99%

“…DVD is rather similar to a DG, but it is more flexible than DG. Different DVD leads to a different scheme, see for instance [20,21,29]. However, DVDM is generally second order in time.…”

Section: Introductionmentioning

confidence: 99%

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Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation

Feng

Dai

2022

Numerical Methods Partial

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In this paper, three high-order accurate and unconditionally energy-stable methods are proposed for solving the conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier. One is developed based on an energy linearization Runge-Kutta (EL-RK) method which combines an energy linearization technique with a specific class of RK schemes, the other two are based on the Hamiltonian boundary value method (HBVM) including a Gauss collocation method, which is the particular instance of HBVM, and a general class of cases. The system is first discretized in time by these methods in which the property of unconditional energy stability is proved. Then the Fourier pseudo-spectral method is employed in space along with the proofs of mass conservation. To show the stability and validity of the obtained schemes, a number of 2D and 3D numerical simulations are presented for accurately calculating geometric features of the system. In addition, our numerical results are compared with other known structure-preserving methods in terms of numerical accuracy and conservation properties.

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Section: Spinodal Decomposition In 2dmentioning

confidence: 99%