一维非线性系统FPK方程的TVD Runge-Kutta WENO型差分解  

SOLUTION OF TVD RUNGE-KUTTA AND WENO SCHEME TO THE FPK EQUATIONS OF ONE-DIMENSION NONLINEAR SYSTEM

作　　者：王文杰[1] 封建湖[1] Wang Wenjie;Feng Jianhu(School of Science of Chang＇an University,Xi＇an 710064,China)

机构地区：[1]长安大学理学院数学系,西安710064

出　　处：《动力学与控制学报》2018年第3期206-210,共5页Journal of Dynamics and Control

摘　　要：首先研究了非线性随机动力系统所对应的Fokker-Planck-Kolmogorov(FPK)方程.其次,讨论了微分方程的三阶TVD Runge-Kutta关于时间的离散差分格式以及关于空间离散的五阶Weighted Essentially nonOscillatory(WENO)差分格式,并将其相结合,得到FPK方程的TVD Runge-Kutta WENO差分解,并与FPK方程的精确解进行了比较.数值结果表明,该方法具有良好的稳定性,且可以解决其他方法在概率密度峰值处偏小,而在尾部处较大等缺点.Firstly,the Fokker-Planck-Kolmogorov equations for nonlinear stochastic dynamic system was studied.Secondly,the third-order TVD Runge-Kutta time difference scheme for differitial equations and the fifth-order WENO scheme for differitial operators were discussed. Moreover,the third-order TVD Runge-Kutta difference scheme was combined with the fifth-order WENO scheme,and the numerical solution for FPK equations using the TVD Runge-Kutta WENO scheme was obtained. Finally,the numerical solution was compared with the analytic solution for FPK equations. The numerical method was shown to give accurate results and overcome the difficulties of other methods,i. e.,the probability density function is too small for the peak while too large for the tailed value.

关 键 词：非线性系统 FPK方程 有限差分法 TVD龙格-库塔格式 ENO格式 WENO格式 

分 类 号：O241.7[理学—计算数学]