Implicit numerical approximation scheme for the fractional Fokker–Planck equation

Wu, Chunhong; Lu, Linzhang

doi:10.1016/j.amc.2010.03.024

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…In order to show that our algorithm is more accurate than the INAM [51], in Table 1, we give the maximum absolute errors (MAEs) at θ 1 = ϑ 1 = 0, θ 2 = ϑ 2 = 1 2 with different values of β and N = M = 20 and compare the achieved results with those obtained using the INAM [51]. Moreover, Table 2 lists the MAEs at θ 1 = ϑ 1 = 0, θ 2 = ϑ 2 = 1 2 with different values of β and N = M = 20.…”

Section: Numerical Resultsmentioning

confidence: 98%

“…Wu and Lu [51] introduced this problem and applied the implicit numerical approximation method (INAM) for obtaining its numerical solution. In order to show that our algorithm is more accurate than the INAM [51], in Table 1, we give the maximum absolute errors (MAEs) at θ 1 = ϑ 1 = 0, θ 2 = ϑ 2 = 1 2 with different values of β and N = M = 20 and compare the achieved results with those obtained using the INAM [51].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Also, in [47], the authors introduced the fully discrete Galerkin finite element method for approximating the solution of the S-FFPE, while in [48], the author introduced a numerical approach based on the [3,3] Padé approximation for solving the S-FFPEs. Other different numerical techniques have been applied for solving T-FFPEs, S-FFPEs and T-SFFPEs, such as the operational tau method [49], the homotopy perturbation method [50], the implicit numerical approximation method [51] and others [52,53].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations

et al. 2015

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In this article, we construct a new numerical approach for solving the time-fractional FokkerPlanck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the timespace-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.

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Section: Numerical Resultsmentioning

confidence: 98%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations

et al. 2015

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“…These methods are second and first order accurate in space, respectively, and both are of order

2 - α

in time. Wu and Lu derived a backward Euler type method for the solution of and proved it to be second order accurate in space and first order accurate in time.…”

Section: Introductionmentioning

confidence: 99%

A backward euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation

Fairweather

Zhang

Yang

et al. 2014

Numer. Methods Partial Differential Eq.

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We formulate and analyze a novel numerical method for solving a time-fractional Fokker-Planck equation which models an anomalous subdiffusion process. In this method, orthogonal spline collocation is used for the spatial discretization and the time-stepping is done using a backward Euler method based on the L1 approximation to the Caputo derivative. The stability and convergence of the method are considered, and the theoretical results are supported by numerical examples, which also exhibit superconvergence.where I = (0, 1), κ 1 > 0 denotes the diffusion coefficient, η 1 > 0 is the friction coefficient, V (x) is an external potential field, and w(x, t) denotes the probability density function. In diffusion

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Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. II. Numerical Simulations

Ercan

Kavvas

2015

J. Hydrol. Eng.

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Implicit numerical approximation scheme for the fractional Fokker–Planck equation

Cited by 5 publications

References 20 publications

A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations

A Jacobi Gauss–Lobatto and Gauss–Radau collocation algorithm for solving fractional Fokker–Planck equations

A backward euler orthogonal spline collocation method for the time-fractional Fokker-Planck equation

Fractional Governing Equations of Diffusion Wave and Kinematic Wave Open-Channel Flow in Fractional Time-Space. II. Numerical Simulations

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