The design of new high-order group iterative method in the solution of two-dimensional fractional cable equation

Khan, Muhammad Asim; Ali, Norhashidah Hj. Mohd.; Hamid, Nur Nadiah Abd

doi:10.1016/j.aej.2021.01.008

Cited by 5 publications

(2 citation statements)

References 29 publications

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“… 2022a ), two-dimensional fractional cable equation (Salama and Abd Hamid 2020 ; Khan et al. 2021 ), two-dimensional fractional reaction diffusion equation (Abdi et al. 2021a ) and two-dimensional fractional advection diffusion equation (Salama et al.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

et al. 2023

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The time-fractional advection–diffusion reaction equation (TFADRE) is a fundamental mathematical model because of its key role in describing various processes such as oil reservoir simulations, COVID-19 transmission, mass and energy transport, and global weather production. One of the prominent issues with time fractional differential equations is the design of efficient and stable computational schemes for fast and accurate numerical simulations. We construct in this paper, a simple and yet efficient modified fractional explicit group method (MFEGM) for solving the two-dimensional TFADRE with suitable initial and boundary conditions. The proposed method is established using a difference scheme based on L1 discretization in temporal direction and central difference approximations with double spacing in spatial direction. For comparison purposes, the Crank–Nicolson finite difference method (CNFDM) is proposed. The stability and convergence of the presented methods are theoretically proved and numerically affirmed. We illustrate the computational efficiency of the MFEGM by comparing it to the CNFDM for four numerical examples including fractional diffusion and fractional advection–diffusion models. The numerical results show that the MFEGM is capable of reducing iteration count and CPU timing effectively compared to the CNFDM, making it well-suited to time fractional diffusion equations.

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Section: Introductionmentioning

confidence: 99%

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

et al. 2023

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“…This is useful for long time simulations, especially when attempting to solve multi-dimensional fractional problems [33][34][35][36]. It is well known that explicit group methods can diminish the computational complexity and reduce the computational time of numerical algorithms effectively [37][38][39][40][41][42][43][44]. However, numerical approximations based on explicit group methods for fractional mobile/immobile equations are still at an early stage of development.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Two-Dimensional Time Fractional Mobile/Immobile Equation Using Explicit Group Methods

Salama

Ali

2022

Int. J. Appl. Comput. Math

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In this paper, we shall present the development of two explicit group schemes, namely, fractional explicit group (FEG) and modified fractional explicit group (MFEG) methods for solving the time fractional mobile/immobile equation in two space dimensions. The presented methods are formulated based on two Crank-Nicolson (C-N) finite difference schemes established at two different grid spacings. The stability and convergence of order O(τ 2−α + h 2 ) are rigorously proven using Fourier analysis. Several numerical experiments are conducted to verify the efficiency of the proposed methods. Meanwhile, numerical results show that the FEG and MFEG algorithms are able to reduce the computational times and iterations effectively while preserving good accuracy in comparison to the C-N finite difference method.

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A higher order unconditionally stable numerical technique for multi-term time-fractional diffusion and advection–diffusion equations

Choudhary,

Singh,

Kumar

2024

Comp. Appl. Math.

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The design of new high-order group iterative method in the solution of two-dimensional fractional cable equation

Cited by 5 publications

References 29 publications

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation

Numerical Solution of Two-Dimensional Time Fractional Mobile/Immobile Equation Using Explicit Group Methods

A higher order unconditionally stable numerical technique for multi-term time-fractional diffusion and advection–diffusion equations

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