A fast difference scheme for the multi-term time fractional advection–diffusion equation with a non-linear source term

Dwivedi, Himanshu Kumar; Rajeev,

doi:10.1016/j.cjph.2024.02.051

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…Equations including multi-term time-fractional derivatives offer for more accurate modeling of the dispersion of pollutants in air and groundwater in environmental engineering by taking into consideration the influence of several transport modes, including advection, diffusion, and dispersion, as well as long-term memory effects. Partial differential equations including multi term time fractional derivatives finds numerous applications in many scientific and engineering domains, for example, the contamination in groundwater [17], the oxygen diffusion from capillary to tissues [18], the anomalous diffusion phenomena [19], the diffusive waves in viscoelastic solids [20], and many other phenomena in physics and biology [21].…”

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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