有限差分法によるFokker-Planck方程式の数値解析 : 第1報, 1自由度非線形系の解析

概要

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The finite difference method is applied to calculate the non Gaussian probability density function of a single DOF nonlinear system subjected to white noise excitation. The probability density function is governed by linear partial differential equation known as the Fokker-Planck equation. The standard finite difference method is not necessarily suitable for the Fokker-Planck equation, since the 1st order upwind difference needs a large number of nodal points and computation time, and the conventional higher order upwind difference and centered difference may cause negative probability. Therefore the 2nd order upwind difference is modified in order to avoid negativeprobability and employed for the drift terms of the Fokker Planck equation. The present scheme also satisfies conservation property, i.e., total probability always equal to One. The stationary joint probability densities of a Duffing and a Van der PoI oscillator are calculated and compared with the exact solution or Monte Carlo simulation results.
一般社団法人日本機械学会の論文
1999-06-25