Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics

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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.

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Palavras-chave: Fokker-Planck Equation, Parabolic partial differential equation, Integrated Radial Basis Functions, Collocation point.,

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DOI: 10.5151/meceng-wccm2012-19433

Referências bibliográficas
  • [1] Mai-Duy N., Tran-Cong T., “Numerical solution of differential equations using multiquadric radial basis function networks”. Neural Networks 14, 185-199, 200
  • [2] Risken, H., “The Fokker-Planck equation: method of solution and applications”, 1989, Springer Verlag Berlin.
  • [3] Zorzano M. P., Mais H., Vazquez L., “Numerical solution of two-dimensional Fokker- Planck equations”. Appl. Math. Comput. 98, 109-17, 1999.
  • [4] Dehghan M., Tatari M., “The use of He’s variational iteration method for solving a Fokker-Planck equation”. Phys. Scr. 74, 310-6, 2006.
  • [5] Odibat Z., Momani S., “Numerical solution of Fokker-Planck equation with space and time fractional derivatives”. Phys. Lett. A 369, 349358, 2007.
  • [6] Harrison G. Numer. Meth. “Numerical solution of the Fokker-Planck equation using moving finite elements”. Part. Diff. Eqs. 4, 219-32, 1988.
  • [7] Jafari M. A., Aminataei A. “Application of homotopy perturbation method in the solution of Fokker-Planck equation”. Phys. Scr. 80, 055001, 2009.
  • [8] Fasshauer G. E., Meshfree approximation methods with Matlab (Interdisciplinary Mathematical Sciences Vol. 6, World Scientific, Singapore, 2007.
  • [9] Kansa E., “Multiquadrics a scattered data approximation scheme with applications to computational fluid dynamics-I: Surface approximations and partial derivatives estimates”. Computers Andamp; Mathematics with Applications 19, 127145, 1990.
  • [10] Kansa E. J., “A scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations’. Comput. Math. Appl. 19, 147-161, 1990.
  • [11] Sarler B., Vertnik R., “Meshfree explicit local radial basis function collocation method for diffusion problems”. Comput. Math. Appl. 51, 1269-1282, 2006.
  • [12] Divo E., Kassab A., “Iterative domain decomposition mesh-less method modeling of incompressible viscous flows and conjugate heat transfer”. Eng. Anal. Boundary Elements 30, 465-478, 2006.
  • [13] Mai-Duy N., Tran-Cong T., “A Control Volume Technique Based on Integrated RBFNs for the Convection-Diffusion Equation”. Numerical methods for partial differential equations 26, 426447, 2010.
  • [14] Franke R., “Scattered data interpolation: tests of some methods”. Mathematics of Computation 38, 181200, 1982.
  • [15] Haykin S., Neural networks: A comprehensive foundation. New Jersey:Prentice Hall, 1999.
  • [16] Kazem S., Rad J. A., Parand K., “Radial basis functions methods for solving Fokker- Planck equation”. Engineering Analysis with Boundary Elements 36, 181-189, 2012.
  • [17] Tatari M., Dehghan M., Razzaghi M., “Application of the Adomian decomposition method for the Fokker-Planck equation”. Math Comput Model 45, 639-50, 2007.
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 2358-0828, DOI 10.5151/meceng-wccm2012-19433

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