0428793 - ÚTAM 2015 RIV GB eng J - Journal Article
Náprstek, Jiří - Král, Radomil
Finite element method analysis of Fokker-Plank equation in stationary and evolutionary versions.
Advances in Engineering Software. Roč. 72, June (2014), s. 28-38. ISSN 0965-9978. E-ISSN 1873-5339
R&D Projects: GA ČR(CZ) GA103/09/0094; GA AV ČR(CZ) IAA200710902
Institutional support: RVO:68378297
Keywords : Fokker-Planck equation * numerical solution * transition effects * stochastic mechanics * probability density function * non-linear dynamic systems
Subject RIV: JM - Building Engineering
Impact factor: 1.402, year: 2014 ; AIS: 0.549, rok: 2014
Result website:
https://doi.org/10.1016/j.advengsoft.2013.06.016DOI: https://doi.org/10.1016/j.advengsoft.2013.06.016

The problems that often arise in stochastic dynamics can be investigated using the Fokker–Planck (FP) equation. The response of a such systems being subjected to additive and/or multiplicative random noise is represented by probability density function (PDF) that gives the full information about a response random character. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful alternative. In particular the Finite Element Method (FEM) seems to be very effective. A couple of single dynamic linear/ non-linear (Duffing and Van Der Pol type) systems under additive and multiplicative random excitations are discussed using FEM as a solution tool of the FP equation. The resulting PDFs are analyzed and if the analytic results exist mutually compared.
Permanent Link: http://hdl.handle.net/11104/0234147