论文标题
随机哈密顿局部微分方程的三种新型多隔离方法
Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations
论文作者
论文摘要
具有多透明保护定律的随机哈密顿部分偏微分方程是重要且相当大的系统。遗传随机哈密顿局部微分方程的几何特征的多隔离方法提供了具有更好的数值稳定性的数值近似值，并且对于获得正确的数值结果至关重要。在本文中，我们提出了三种基于局部径向基础函数搭配方法，分裂技术和分区的runge-kutta方法的新型多隔离方法，用于随机哈密顿局部偏微分方程。提出了针对非线性随机波程，随机非线性schrödinger方程，随机Korteweg-de Vries方程和随机的Maxwell方程的混凝土数值方法。我们以随机波方程为例，以执行数值实验，这表明了所提出的方法的有效性。
Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide numerical approximations with better numerical stability, and are of vital significance for obtaining correct numerical results. In this paper, we propose three novel multi-symplectic methods for stochastic Hamiltonian partial differential equations based on the local radial basis function collocation method, the splitting technique, and the partitioned Runge-Kutta method. Concrete numerical methods are presented for nonlinear stochastic wave equations, stochastic nonlinear Schrödinger equations, stochastic Korteweg-de Vries equations and stochastic Maxwell equations. We take stochastic wave equations as examples to perform numerical experiments, which indicate the validity of the proposed methods.
