An efficient linearly-implicit energy-preserving scheme with fast solver for the fractional nonlinear wave equation
An efficient linearly-implicit energy-preserving scheme with fast solver for the fractional nonlinear wave equation
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DOI：
10.3934/math.20231358
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发表时间：
2023
期刊：
影响因子：
2.2
通讯作者：
Tingting Ma;Yuehua He
中科院分区：
文献类型：
--
作者：
Tingting Ma;Yuehua He
本文考虑了非线性波动方程的Hamilton结构，并对分数阶Laplacian算子构造了有效的能量保持格式。为此，我们首先利用分数阶变分导数推导出方程的Hamilton形式，然后对原方程应用有限差分方法得到半离散的Hamilton系统。进一步，利用标量辅助变量法和外推技术逼近半离散方程组，构造了一种高效的线性隐式能量守恒格式。提出了一种快速求解器，以减少CPU的消耗。最后通过数值计算验证了格式的有效性和守恒性。
The paper considers the Hamiltonian structure and develops efficient energy-preserving schemes for the nonlinear wave equation with a fractional Laplacian operator. To this end, we first derive the Hamiltonian form of the equation by using the fractional variational derivative and then applying the finite difference method to the original equation to obtain a semi-discrete Hamiltonian system. Furthermore, the scalar auxiliary variable method and extrapolation technique is used to approximate a semi-discrete system to construct an efficient linearly-implicit energy-preserving scheme. A fast solver for the proposed scheme is presented to reduce CPU consumption. Ample numerical results are given to finally confirm the efficiency and conservation of the developed scheme.