An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations
An efficient linearly implicit and energy‐conservative scheme for two dimensional Klein–Gordon–Schrödinger equations
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DOI：
10.1002/num.23064
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发表时间：
2023-08
影响因子：
3.9
通讯作者：
Hongwei Li;Yuna Yang;Xiangkun Li
中科院分区：
文献类型：
--
作者：
Hongwei Li;Yuna Yang;Xiangkun Li
Klein-Gordon-Schrödinger方程描述了物理中核子场与介子场相互作用的经典模型，如何设计能量守恒和稳定的格式是一个重要的问题。本文旨在为Klein-Gordon-Schrödinger方程建立一个线性化、能量守恒、无条件稳定和有效的格式。利用一些辅助变量绕过Klein-Gordon-Schrödinger方程的虚函数，将原系统转化为其实数形式。基于不变能量二次化方法，通过引入拉格朗日乘子，推导出了一个等效系统。然后设计了有效且无条件稳定的格式对所推导的等价系统进行离散化。对所提出的格式进行了数值分析，以说明其唯一的可解性和收敛特性。数值算例验证了所提方法的精度、能量守恒定律、质量守恒定律和稳定性。
The Klein–Gordon–Schrödinger equations describe a classical model of interaction of nucleon field with meson field in physics, how to design the energy conservative and stable schemes is an important issue. This paper aims to develop a linearized energy‐preserve, unconditionally stable and efficient scheme for Klein–Gordon–Schrödinger equations. Some auxiliary variables are utilized to circumvent the imaginary functions of Klein–Gordon–Schrödinger equations, and transform the original system into its real formulation. Based on the invariant energy quadratization approach, an equivalent system is deduced by introducing a Lagrange multiplier. Then the efficient and unconditionally stable scheme is designed to discretize the deduced equivalent system. A numerical analysis of the proposed scheme is presented to illustrate its uniquely solvability and convergence. Numerical examples are provided to validate accuracy, energy and mass conservation laws, and stability of our proposed method.