Abstract
The Fokker–Planck–Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or non-linear system to random excitation. This paper proposes a numerical method for calculating the stationary solution of the FPK equation, which is based upon the weighted residual approach using Shannon wavelets as shape functions. The method is developed here for an n -dimensional system and its relationship with the distributed approximating functional (DAF) approach is investigated. For the purposes of validation, numerical results obtained using the proposed method are compared with available exact solutions and numerical solutions for some non-linear oscillators. For the systems considered excellent results over the main body and tails of the marginal distributions are obtained. The accuracy and efficiency of the method are investigated in comparison to the finite element method (FEM).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
