Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis

Marasi, Hamidreza; Derakhshan, Mohammadhossein

doi:10.1016/j.matcom.2022.09.020

Cited by 4 publications

(3 citation statements)

References 38 publications

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“…The method converges at a rate of 4 and it was demonstrated that the suggested algorithm is unconditionally stable, even for events involving a harmonic external force and viscous damping. Marasi and Derakhshan [197] developed the approximate technique involving finite difference and Hermite quintic collocation algorithms for a variable-order time fractional mobile-immobile advection-dispersion model:…”

Section: Application Of Hermite As a Basis Functionmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article.

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Section: Application Of Hermite As a Basis Functionmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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“…Nowadays, differential equations of fractional order as extension of the differential equations of integer order play a fundamental role in the modeling of many scientific, practical, and important problems [1][2][3][4][5][6][7][8][9][10]. Recently, several numerical methods have been proposed to simulate various types of fractional-order systems [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…t in which b  t denotes the Riemann-Liouville fractional integral for different wavelets of order β, and Q β shows the operational matrix to the Riemann-Liouville integral operator. For computing Q β in equation (1), first, these wavelets were extended into block-pulse functions, then the operational matrix of the Riemann-Liouville integral of block-pulse functions is applied to discovering Q β . In this paper, we propose an effective numerical method, based on the use of two-dimensional Shifted fractional-order Gegenbauer Multi-wavelets, for finding the approximate solutions of the time-fractional distributed order non-linear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

et al. 2023

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In this paper, we propose an effective numerical method, based on the use of two-dimensional Shifted fractional-order Gegenbauer Multi-wavelets, for finding the approximate solutions of the time-fractional distributed order non-linear partial differential equations. The method is applied to solve fractional distributed order non-linear Klein-Gordon equation, numerically. We derive an exact formula for the Riemann–Liouville fractionalintegral operator for the Shifted fractional Gegenbauer Multi-wavelets.Applying function approximations obtained by this method turns the considered equation into a system of algebraic equations. Error estimation and convergence analysis of the methodare also studied. Some numerical examples are included to show and check the effectiveness of the proposed method.

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An efficient hybrid approach for numerical study of two-dimensional time-fractional Cattaneo model with Riesz distributed-order space-fractional operator along with stability analysis

Derakhshan,

Mortazavifar,

Veeresha

et al. 2024

Phys. Scr.

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In this article, we study and analyze the two-dimensional time-fractional Cattaneo model with Riesz space distributed-order. To obtain approximate solutions of this type of fractional model the combined and eﬀective numerical approach based on the ADI Galerkin method and the Legendre spectral method used the ADI Galerkin numerical method uses the ﬁnite diﬀerence approach. The ADI Galerkin numerical method is used to approximate the proposed model in terms of the time variable, and the Legendre spectral method is applied to discretize the fractional model with respect to the space variable. Also, the convergence analysis and stability of the proposed method are discussed and reviewed in this manuscript. In the end, some numerical examples are tested for the eﬀectiveness and accuracy of the proposed method.

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Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis

Cited by 4 publications

References 38 publications

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

An efficient numerical method for the time-fractional distributed order nonlinear Klein–Gordon equation with shifted fractional Gegenbauer multi-wavelets method

An efficient hybrid approach for numerical study of two-dimensional time-fractional Cattaneo model with Riesz distributed-order space-fractional operator along with stability analysis

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