Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition

Zhang, Biao; Bu, Weiping; Xiao, Aiguo

doi:10.1007/s11075-021-01102-z

Cited by 6 publications

(2 citation statements)

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“…Anomalous diffusion describes many physical phenomena like protein diffusion within cells or diffusion across porous media. Besides, anomalous diffusion was detected in scalar mixing in the interstellar medium [14], harmonic spring-mass systems [15,16], moisture transport in cement-based materials [17], and ion channels in the plasma membrane [18]. The daily fluctuations of the climate variables like the temperature can be considered as steps of a random walker in anomalous diffusion equations [19].…”

Section: Introductionmentioning

confidence: 99%

“…Authors in [27] offered a numerical approach to solve fractional anomalous diffusion by applying the Petrov-Galerkin technique based on Jacobi polynomials as the trial and test space. In [17], a technique based on the L 1 -method was proposed for discretizing space and time to compute the numerical solution of the space-time fractional diffusion equation. In [28,29], a numerical algorithm was proposed for solving fractional diffusion equations using a spectral/ element method combined with a matrix transfer technique (MTT).…”

Section: Introductionmentioning

confidence: 99%

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An efficient approach for solving a class of fractional anomalous diffusion equation with convergence

Rashidinia,

Molavi-Arabshahi,

Yousefi

2024

Phys. Scr.

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This article presents a study on Fractional Anomalous Diﬀusion (FAD) and proposes a novel numerical algorithm for solving Cupoto’s type fractional sub-diﬀusion equations. to convert the fractional model into a set of nonlinear algebraic equations. These equations are eﬃciently solved using the Levenberg-Marquardt algorithm. The study provides the error analysis to validate the proposed method. The eﬀectiveness and accuracy of the method are demonstrated through several test problems, and its performance and reliability are compared with other existing methods in the literature. The results indicate that the proposed method is a reliable and eﬃcient technique for solving fractional sub-diﬀusion equations, with better accuracy and computational eﬃciency than other existing methods. The study’s ﬁndings have important implications for researchers working in the ﬁeld of fractional calculus. They could provide a valuable tool for solving sub-diﬀusion equations in various applications, including physics, chemistry, biology, and engineering.

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