带加性噪声的随机Klein--Gordon--Schrödinger方程的新型保结构格式
Novel structure-preserving schemes for stochastic Klein--Gordon--Schrödinger equations with additive noise
AI总结：
本文针对带加性噪声的随机KGS方程，提出保持平均电荷、平均能量、辛性和多辛性的新型保结构数值格式，并通过数值实验验证了理论结果。
摘要：
随机Klein--Gordon--Schrödinger（KGS）方程是重要的数学模型，描述了随机环境中标量核子与中性标量介子之间的相互作用。本文提出新型保结构格式，数值求解带加性噪声的随机KGS方程，该格式保持平均电荷演化律、平均能量演化律、辛性和多辛性。通过在空间上应用中心差分、sine伪谱法或有限元法，并在时间上修正有限差分，我们为原系统提出了一些保持电荷和能量的全离散格式。此外，结合时间上的辛Runge-Kutta法和空间上的有限差分，我们提出了一类保持随机KGS方程几何结构的多辛离散化方法。最后，数值实验证实了理论发现。
英文摘要：
Stochastic Klein--Gordon--Schrödinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fully-discrete scheme for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings.
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