𝔖 Bobbio Scriptorium
✦   LIBER   ✦

NUMERICAL SOLUTION OF THE STATIONARY FPK EQUATION USING SHANNON WAVELETS

✍ Scribed by S. MCWILLIAM; D.J. KNAPPETT; C.H.J. FOX

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
448 KB
Volume
232
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

✦ Synopsis

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 e$ciency of the method are investigated in comparison to the "nite element method (FEM).

πŸ“œ SIMILAR VOLUMES

EXTREME-VALUE PREDICTION FOR NON-LINEAR
EXTREME-VALUE PREDICTION FOR NON-LINEAR STOCHASTIC OSCILLATORS VIA NUMERICAL SOLUTIONS OF THE STATIONARY FPK EQUATION
✍ J.F. Dunne; M. Ghanbari πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 305 KB

The accuracy of two well-established numerical methods is demonstrated, and the importance of ''bandwidth'' examined, for computationally efficient Markov based extreme-value predictions associated with finite duration stationary sample paths of a non-linear oscillator driven by Gaussian white noise

Numerical solution of nth-order integro-
Numerical solution of nth-order integro-differential equations using trigonometric wavelets
✍ Mehrdad Lakestani; Mahmood Jokar; Mehdi Dehghan πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 219 KB

The main aim of this paper is to apply the trigonometric wavelets for the solution of the Fredholm integro-differential equations of nth-order. The operational matrices of derivative for trigonometric scaling functions and wavelets are presented and are utilized to reduce the solution of the Fredhol

A Wavelet Collocation Method for the Num
A Wavelet Collocation Method for the Numerical Solution of Partial Differential Equations
✍ S. Bertoluzza; G. Naldi πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 355 KB

We describe a wavelet collocation method for the numerical solution of partial differential equations which is based on the use of the autocorrelation functions of Daubechie's compactly supported wavelets. For such a method we discuss the application of wavelet based preconditioning techniques along

Numerical solution of the Poisson-Boltzm
Numerical solution of the Poisson-Boltzmann equation using tetrahedral finite-element meshes
✍ Cortis, Christian M.; Friesner, Richard A. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 252 KB πŸ‘ 2 views

The automatic three-dimensional mesh generation system for molecular geometries developed in our laboratory is used to solve the Poisson᎐Boltzmann equation numerically using a finite element method. For a number of different systems, the results are found to be in good agreement with those obtained