Higher order averaging of linear fokker-planck equations with periodic forcing Articles uri icon

publication date

  • November 2012

start page

  • 1315

end page

  • 1342

issue

  • 4

volume

  • 72

international standard serial number (ISSN)

  • 0036-1399

electronic international standard serial number (EISSN)

  • 1095-712X

abstract

  • We investigate linear Fokker-Planck equations or stochastic Hamiltonian systems with periodic forcing where the impact of deterministic forcing is not captured by classical stochastic averaging. To overcome this problem, a formal energy projection method is introduced, which splits the corresponding Fokker-Planck equation and allows the computation of higher order stochastic averages. Generally, the resulting averages have to be computed with a numerical scheme. We illustrate the results of our method with two examples: the linear oscillator with periodic forcing and a nonlinear oscillator.