用差分法与超松弛迭代法求高维平稳FPK方程的解  

Stationary solutions of high dimensional reduced FPK equation using both finite difference method and successive over-relaxation method

作　　者：黄志龙[1] 张丽强[1] 

机构地区：[1]浙江大学力学系,杭州310027

出　　处：《计算力学学报》2008年第2期177-182,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10672142);新世纪优秀人才支持计划资助项目

摘　　要：用不同精度的差分格式将高维平稳FPK方程离散化为线性代数方程组,然后用超松弛迭代法求解该线性代数方程组得到平稳FPK方程的近似解。讨论了不同的差分格式、网格密度及超松弛因子对解精度及收敛速度的影响,并与其他方法的计算精度进行比较,提出用多重网格算法提高计算效率。研究了典型的二维及四维随机系统的稳态响应,算例表明,该算法具有简洁、节省存储量且精度高的特点,是求解高维平稳FPK方程解的有效算法。The combination of finite difference method and successive over-relaxation method is employed to numerically get the stationary solution of high dimensional reduced Fokker-Planck-Kolmogorov（FPK） equation. The effects of different order of central difference scheme,the mesh density and factor of successive over-relaxation on the convergence and accuracy of numerical solution are discussed. A multimesh iterative method is proposed to improve the efficiency and accuracy of numerical solution. Two examples are given to illustrate the application of the proposed procedures.

关 键 词：差分法 超松弛迭代法 FPK方程 

分 类 号：O324[理学—一般力学与力学基础]