NUMERICAL SOLUTION OF FOKKER-PLANCK EQUATION USING THE INTEGRAL RADIAL BASIS FUNCTION NETWORKS

NUMERICAL SOLUTION OF FOKKER-PLANCK EQUATION USING THE INTEGRAL RADIAL BASIS FUNCTION NETWORKS

Tran, C.-D.; Mai-Duy, N.; Tran-Cong, T.

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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.

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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DOI: 10.5151/meceng-wccm2012-19433

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Como citar:

Tran, C.-D.; Mai-Duy, N.; Tran-Cong, T.; "NUMERICAL SOLUTION OF FOKKER-PLANCK EQUATION USING THE INTEGRAL RADIAL BASIS FUNCTION NETWORKS", p-3540-3548. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-19433