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求解电报方程的自适应重要性抽样蒙特卡罗算法

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求解电报方程的自适应重要性抽样蒙特卡罗算法 洪志敏1,2, 陈雪1, 李强11. 内蒙古工业大学理学院, 呼和浩特 010051;
2. 北京大学数学科学学院, 北京 100871 Numerical Solution of Telegraph Equation Using Adaptive Importance Sampling Monte Carlo Algorithm HONG Zhimin1,2, CHEN Xue1, LI Qiang11. School of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China;
2. School of Mathematical Sciences, Peking University, Beijing 100871, China
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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.
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收稿日期: 2015-09-23
PACS:O242
O212
基金资助:国家自然科学基金(11461051,11361036),高等学校博士学科点专项科研基金(20131514110005)联合资助课题以及内蒙古自然科学基金(2015MS0104)资助项目.
引用本文:
洪志敏, 陈雪, 李强. 求解电报方程的自适应重要性抽样蒙特卡罗算法[J]. 应用数学学报, 2016, 39(6): 859-870. HONG Zhimin, CHEN Xue, LI Qiang. Numerical Solution of Telegraph Equation Using Adaptive Importance Sampling Monte Carlo Algorithm. Acta Mathematicae Applicatae Sinica, 2016, 39(6): 859-870.
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