An extension of the Gegenbauer pseudospectral method for the time fractional Fokker‐Planck equation

Izadkhah, Mohammad Mahdi; Saberi‐Nadjafi, Jafar; Toutounian, Faezeh

doi:10.1002/mma.4656

Cited by 7 publications

(5 citation statements)

References 32 publications

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“…Consequently, in the last decade, the Jacobi polynomials have been widely used to solve fractional problems. [36][37][38][39][40][41][42][43] Our method uses the Jacobi polynomials too. Thus, in this section, we briefly review the Jacobi polynomials, Jacobi quadrature rules, and a relevant theorem on the fractional derivatives of Jacobi polynomials.…”

Section: Preliminaries On Jacobi Polynomialsmentioning

confidence: 99%

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

Almoaeet

Shamsi

Khosravian-Arab

et al. 2019

Math Methods in App Sciences

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We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.

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Section: Preliminaries On Jacobi Polynomialsmentioning

confidence: 99%

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

Almoaeet

Shamsi

Khosravian-Arab

et al. 2019

Math Methods in App Sciences

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“…For the STFFP equation, Zhang et al [34] employed a time-space spectral method with Jacobi polynomials for temporal discretisation and Legendre polynomials for spatial discretisation. A pseudospectral method was discussed in [12,30].…”

Section: Introductionmentioning

confidence: 99%

A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution

Wei Zeng,

Aiguo Xiao,

Weiping Bu

et al. 2020

EAJAM

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An STPG spectral method for TFFP equations with nonsmooth solutions is developed. The numerical scheme is based on generalised Jacobi functions in time and Legendre polynomials in space. The generalised Jacobi functions match the leading singularity of the corresponding problem. Therefore, the method performs better than methods with polynomial bases. The stability and convergence of the method are proved. Numerical experiments confirm the theoretical error estimates.

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“…Javidi et al have proposed the pseudospectral method (PSM), which is also called spectral collocation method [11][12][13]. It is a numerical method widely used to resolve partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

Yuan

et al. 2019

Symmetry

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A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is obtained via dispersing the telegraph equation in space domain by utilizing the pseudospectral method (PSM) based on Chebyshev polynomial. Then the two-step three-order boundary value method (BVM3) is presented and employed to resolve the obtained differential equation, so the numerical solution of the space discrete points can be obtained. Furthermore, the Chebyshev pseudospectral–two-step three-order boundary value coupled method (PSM-BVM3) is presented and compared with the Chebyshev pseudospectral–two-step two order boundary value coupled method (PSM-BVM2), the pseudospectral–differential quadrature method (PSM-DQM), and the pseudospectral method–trapezoid rule (PSM-TR) to validate the feasibility of the new proposed method. Theoretical analysis and numerical simulation reveal that the proposed Chebyshev PSM-BVM3 has a higher performance than the conventional method. For the proposed Chebyshev PSM-BVM3, the higher precision, efficiency, and numerical stability can be obtained and achieved only with fewer discrete points in the space domain, which is suitable for solving the transient response of transmission line. The proposed PSM-BVM3 can improve the drawback of numerical instability of the PSM and can also improve the disadvantage of the BVM as it is not easy to change the latter’s timestep size.

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An extension of the Gegenbauer pseudospectral method for the time fractional Fokker‐Planck equation

Cited by 7 publications

References 32 publications

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution

Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method

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