Solving 2D time‐fractional diffusion equations by a pseudospectral method and Mittag‐Leffler function evaluation

Esmaeili, Shahrokh

doi:10.1002/mma.4101

Cited by 4 publications

(2 citation statements)

References 51 publications

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“…The authors of [41] obtained the solution of timefractional advection diffusion equation using CSM. Esmaeili [42] solve two dimensional time-fractional diffusion equations via a pseudospectral method in a bounded domain. Mittal [43] solved multi-dimensional nonlinear fractional evolution equation via the Jacobi pseudospectral quadrature simulation technique.…”

Section: Introductionmentioning

confidence: 99%

Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation

Ali Shah,

Kamran,

Aljawi

et al. 2024

Phys. Scr.

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Multi-term time-fractional advection diffusion equations are vital for simulating a wide range of physical phenomena, including fluid dynamics and environmental transport processes. However, due to their natural complexity, these equations pose challenges for conventional numerical approaches. In this article, we develop a high order accurate method to solve the multi-term time-fractional advection diffusion equations. We combine the Laplace transform (LT) to integrate the considered equations in time, with Chebyshev spectral method (CSM) for spatial terms. The proposed method produces highly accurate solutions with remarkably low computationalcost as compared to finite difference method. The propose numerical scheme first employs the LT which reduces the considered problem into a finite set of elliptic equations which may be solved in parallel. Then, the CSM is employed for the disctrezation of spatial operators, which makes it possibly to accurately represent the solution chebyshev grid. Finally, numerical inversion of LT is used to convert the obtain solution from the Laplace domain into the real domain. This work utilizes the modified Talbot's method and Stehfest's method for numerical inversion of the LT. To measure the performance, efficiency, and accuracy of the suggested approach, numerical approximations of three models are acquired and verified against the exact solution. The outcomes presented in tables and figures demonstrate that the modified Talbot's method performed better as compared to Stehfest's method.

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Section: Introductionmentioning

confidence: 99%

Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation

Ali Shah,

Kamran,

Aljawi

et al. 2024

Phys. Scr.

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“…As other numerical methods for fractional ADEs, we can refer to Zhai et al, Bhrawy et al, and Li and Deng . For some numerical methods for other equations, which are relevant to fractional ADEs, we can refer the interested readers to Meerschaert and Tadjeran, Dehghan and Abbaszadeh, Feng et al,() Esmaeili, Zaky, and references therein.…”

Section: Introductionmentioning

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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Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)

Kazem

Dehghan

2018

Engineering with Computers

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Solving 2D time‐fractional diffusion equations by a pseudospectral method and Mittag‐Leffler function evaluation

Cited by 4 publications

References 51 publications

Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation

Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation

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

Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)

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