【摘要】 提出一种常系数二阶双曲型电报方程的自适应重要性抽样蒙特卡罗算法.通过使用无条件稳定的紧有限差分格式将电报方程离散化为线性代数系统,对得到的线性系统使用具有动态松弛因子的自适应重要性抽样蒙特卡罗算法,加速了蒙特卡罗算法的收敛.一些数值算例的实现证明了提出方法的有效性和适用性.提出的方法容易且适合在计算机上编程实现,所得数值解接近文献提供的精确解.更多还原

【Abstract】 In this paper,the authors proposed a Monte Carlo algorithm based on adaptive importance sampling to find numerical solutions of second order hyperbolic telegraph equations with constant coefficients.Using unconditionally stable compact finite difference formula,we reduce the telegraph equations to a linear algebraic system.The adaptive importance sampling Monte Carlo algorithm with dynamic relaxation factor is applied to this system and accelerating the convergence of the Monte Carlo algorithm.Some numerical examples are considered to demonstrate the validity and applicability of the proposed scheme.It is easy and suitable for computer implementation and obtains numerical solutions close to the exact solutions and available in the literature.更多还原