Response of stochastic dynamical systems driven by additive Gaussian and Poisson white noise: Solution of a forward generalized Kolmogorov equation by a spectral finite difference method Original Research Article

A numerical method is given for the solution of the probability density function of the response process of memoryless one- and two-state dynamical systems having polynomial restoring forces and which are subjected to a combination of Gaussian and Poisson white noises. The method employs the Fourier transformed forward generalized Kolmogorov equation to arrive at an initial-boundary value problem for the characteristic function, which is solved using a high-order finite difference procedure. The probability density function is recovered by numerical inverse Fourier transformation. Several examples are given, the results of which are compared with, analytical solutions where available and with simulation otherwise.