随机动力学中FPK方程的径向基点插配点方法求解

Radial point collocation method(RPCM) for solving FPK equation in stochastic dynamics

应用径向基点插配点方法对随机动力学中的FPK方程进行了求解。所求未知函数的空间插值采用径向基点插近似,而时间导数离散采用差分格式,建立具有带宽特性的代数方程,采用逐次超松弛迭代法(SOR)有效地求解所得到的代数方程。针对线性振子和杜芬振子问题的FPK方程进行了具体的数值求解,计算结果表明了方法的有效性,尤其是散点模型的计算结果表明该方法具有比其它有网格数值方法对非规则离散模型适应性更强的优点。

This paper applies radial point collocation method （RPCM） for solving FPK equations arising in nonlinear stochastic dynamics. The unknown function is approximated by radial point interpolation method in space discretization, and difference schemes are adopted in time discretization. The algebraic system equations with bandwidth character are built, and it is effectively solved by successive over-relaxation （SOR） method. The numerical results for the FPK equation of linear and Dulling oscillators demonstrate that a good accuracy can be obtained with both the uniform model and the scattered point model.