Cubic B-spline Interpolation Method Research Articles

Transient and stationary response statistics of van der Pol oscillators subjected to broad band random excitation

The joint probability density function of the state space vector of a white noise excited van der Pol oscillator satisfies a Fokker-Planck-Kolmogorov (FPK) equation. The paper describes a numerical procedure for solving the transient FPK equation based on the path integral solution (PIS) technique. It is shown that by combining the PIS with a cubicB-spline interpolation method, numerical solution algorithms can be implemented giving solutions of the FPK equation that can be made accurate down to very low probability levels. The method is illustrated by application to two specific examples of a van der Pol oscillator.