Efficient space-time Jacobi rational spectral methods for second order time-dependent problems on unbounded domains

Zhang, Tiangong; Li, Huiyuan; Wang, Zhongqing

doi:10.1016/j.apnum.2022.02.012

Cited by 4 publications

(1 citation statement)

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“…Fractional calculus is one of the important topics in science, engineering, physics, and other disciplines due to its representation in the mathematical model of natural events [1]. The spectral method is considered a well-known numerical method to approximate the solution of various fractional differential equations (FDEs) [2][3][4] and fractional integral equations (FIEs) [5][6][7]. Because of the ability to apply and adjust over both finite and infinite intervals and rapid rate convergence with relatively few grid points, making them computationally efficient [8].…”

Section: Introductionmentioning

confidence: 99%

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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