A study of an efficient numerical method for solving the generalized fractional reaction-diffusion model involving a distributed-order operator along with stability analysis

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED Computers & Mathematics with Applications Pub Date : 2024-12-18 DOI:10.1016/j.camwa.2024.12.006
Muhammad Suliman , Muhammad Ibrahim , Ebrahem A. Algehyne , Vakkar Ali
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Abstract

In this manuscript, we study a generalized fractional reaction-diffusion model involving a distributed-order operator. An efficient hybrid approach is proposed to solve the presented model. The L1 approximation is utilized to discretize the time variable, while the mixed finite element method is employed for spatial discretization. A detailed error and stability analysis of the proposed method is provided. Furthermore, we prove that the computational accuracy achieved by the proposed approach is of order O(h2+(Δt)3ξmax). To validate and evaluate the numerical approach, three numerical experiments are conducted, with results presented through graphs and tables.
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涉及分布阶算子的广义分数阶反应扩散模型的有效数值求解方法研究及稳定性分析
在本文中,我们研究了一个涉及分布阶算子的广义分数反应扩散模型。提出了一种有效的混合方法来求解该模型。采用L1近似对时间变量进行离散,采用混合有限元法对空间变量进行离散。对该方法进行了详细的误差分析和稳定性分析。此外,我们证明了该方法的计算精度为O(h2+(Δt)3−ξmax)阶。为了验证和评价数值方法,进行了三个数值实验,并以图表的形式给出了结果。
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来源期刊
Computers & Mathematics with Applications
Computers & Mathematics with Applications 工程技术-计算机:跨学科应用
CiteScore
5.10
自引率
10.30%
发文量
396
审稿时长
9.9 weeks
期刊介绍: Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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