二阶FPK方程的概率密度演化分析  

Probability Density Evolution of Second-Order FPK Equations

作　　者：孙鹏 刘建华[1] 姜文安 吴杰[1] SUN Peng;LIU Jianhua;JIANG Wenan;WU Jie(Department of Engineering Mechanics,Jiangsu University of Science and Technology,212003,Zhenjiang,Jiangsu,PRC)

机构地区：[1]江苏科技大学工程力学系,江苏镇江212003

出　　处：《江西科学》2018年第5期709-715,736,共8页Jiangxi Science

基　　金：国家自然科学基金项目(11702119);江苏省自然科学基金项目(BK20170565和BK20170581)

摘　　要：给出求解二阶FPK方程的一种隐式有限差分格式,研究了四类不同振子的非平稳解。基于隐式有限差分格式,考察了各系统的瞬态概率密度函数,研究了边缘概率密度函数和联合概率密度函数随时间的演化历程。利用Monte Carlo数值仿真验证了本文近似方法的正确性。In this paper, an implicit finite difference scheme for solving second-order FPK equations is presented. The non-stationary response of four types of oscillators are studied. Based on the implicit finite difference method, the transient probability density function of each system is investigated. The evolution of marginal probability density function and joint probability density function is discussed. This approximate method is verified by the Monte Carlo numerical simulations.

关 键 词：FPK方程 瞬态解 有限差分法 MONTE Carlo仿真 

分 类 号：O241.8[理学—计算数学]