Methodological Approaches for the Fokker–Planck Equation Associated to Nonlinear Stochastic Differential Systems with Uncertain Parameters
Mohamed Ben Said
MMC, Department of Applied Mathematics
Faculty of Sciences and Techniques Tangier, Morocco
bensaidmoh1970@yahoo.fr
Ihsane Salleh
M2CS, Research Center STIS
Department of Applied Mathematics and Information, ENSET
Mohammed V University, Rabat, Morocco
ihsane.salleh@um5s.net.ma
Lahcen Azrar
M2CS, Research Center STIS
Department of Applied Mathematics and Information, ENSET
Mohammed V University, Rabat, Morocco
and
Department of Mechanical Engineering
Faculty of Engineering KAU, Jeddah, Saudi Arabia
Abstract
This paper is an extension of work originally presented at the World Conference on Complex Systems. In this paper, methodological approaches and numerical procedures are elaborated for nonlinear stochastic differential equations with uncertain parameters. The associated Fokker–Planck equation is used to get the distribution function. Mathematical developments based on the meshfree method with radial basis functions and on exponential closure combined with Monte Carlo and conditional expectation methods are elaborated for numerical solutions. The obtained approximate solutions compare well with available solutions and the effectiveness and accuracy of the proposed methods are demonstrated.
Keywords: exponential closure method; meshfree method; radial basis function; Fokker–Planck equation; stochastic differential equation; uncertain parameters; probability density function; Monte Carlo; conditional expectation
Cite this publication as:
M. B. Said, I. Salleh and L. Azrar, “Methodological Approaches for the Fokker–Planck Equation Associated to Nonlinear Stochastic Differential Systems with Uncertain Parameters,” Complex Systems, 28(4), 2019 pp. 411–431.
https://doi.org/10.25088/ComplexSystems.28.4.411
