Numerical solution of Fokker-Planck equation using the integral radial basis function networks

Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T. (2012) Numerical solution of Fokker-Planck equation using the integral radial basis function networks. In: 10th World Congress on Computational Mechanics (WCCM 2012), 8-13 Jul 2012, Sao Paulo, Brazil.

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Abstract

The Fokker Planck Equation (FPE) is a partial differential equation for the probability density and transition probability of a random process. Owing to its broad range of
applications, the FPE has been an interesting research topic. Recently, Radial basis functions (RBFs) have emerged as a powerful numerical tool for solving partial differential equations and this paper reports an integrated RBFs (IRBFs) based numerical method for the solution of
FPEs. The use of integration to construct RBF approximants helps avoid the reduction in convergence rate caused by differentiation [1]. Numerical experiments showed that IRBF methods can yield accurate solutions on a much coarser mesh, thus reducing the computational effort required for a given degree of accuracy.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: This publication is copyright. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 15 Apr 2013 03:16
Last Modified: 11 Nov 2015 02:30
Uncontrolled Keywords: Fokker-Planck equation; parabolic partial differential equation; integrated radial basis functions; collocation point
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.5151/10.5151/meceng-wccm2012-19433
URI: http://eprints.usq.edu.au/id/eprint/23079

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