Radial basis functions methods for solving Fokker–Planck equation

Kazem, Saeed; Rad, Jamal Amani; Parand, Kourosh

doi:10.1016/j.enganabound.2011.06.012

Cited by 54 publications

(42 citation statements)

References 52 publications

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“…The present method is verified with some numerical experiments which have been described in [4,16,17]. It is worth noting that the problems are solved on a bounded interval which is uniformly discretized.…”

Section: Numerical Examplesmentioning

confidence: 70%

Numerical Solution of Fokker-Planck Equation Using the Integral Radial Basis Function Networks

Tran¹,

Mai‐Duy²,

Tran-Cong³

2014

Proceedings of 10th World Congress on Computational Mechanics

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Section: Numerical Examplesmentioning

confidence: 70%

Numerical Solution of Fokker-Planck Equation Using the Integral Radial Basis Function Networks

Tran¹,

Mai‐Duy²,

Tran-Cong³

2014

Proceedings of 10th World Congress on Computational Mechanics

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“…Compared to the FEM and the BEM, this type of method is meshless, and the approximate solutions are constructed based on a cluster of scattered nodes [30][31][32][33][34][35][36]. Many meshless methods are derived from a weak-form formulation on global domain or a set of local sub-domains.…”

Section: Introductionmentioning

confidence: 99%

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Rad

Parand

Abbasbandy

2015

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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In this paper, a method for the numerical pricing of American and European options under the Black-Scholes model is introduced. This approach is meshless local Petrov-Galerkin (MLPG) based on local weak form and the moving least squares approximations. The MLPG offers advantages over conventional and strong meshless methods of radial basis function approximations. In this paper, the American option which is a free boundary problem, is reduced to a fixed boundary problem using a Richardson extrapolation technique. Then a time stepping method is employed for the time derivative. Finally numerical results are presented in two test cases. These experiments show that MLPG approach is accurate and fast, and performs significantly better compared to the conventional radial basis functions collocation methods.

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“…Authors of [2] investigated the application of Adomian decomposition method for solving Fokker-Planck equation. In [9] two numerical meshless methods based on radial basis function are presented. In [10] homotopy perturbation method (HPM) was considered to solve the linear and nonlinear Fokker-Planck equation.…”

Section: Introductionmentioning

confidence: 99%

Meshless method for the numerical solution of the Fokker–Planck equation

Askari

Adibi

2015

Ain Shams Engineering Journal

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In this paper numerical meshless method for solving Fokker-Planck equation is considered. This meshless method is based on multiquadric radial basis function and collocation method to approximate the solution. Here we apply h-weighted finite difference method. The stability analysis of the method is dealt with, using a linearized stability method. Numerical examples illustrate the validity and applicability of the method. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Radial basis functions methods for solving Fokker–Planck equation

Cited by 54 publications

References 52 publications

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

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Meshless method for the numerical solution of the Fokker–Planck equation

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