L1-FEM discretizations for two-dimensional multiterm fractional delay diffusion equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-17 DOI:10.1016/j.cnsns.2024.108285

引用次数: 0

Abstract

A two-dimensional multiterm fractional delay diffusion equation is considered. The representation of the exact solution of the equation is derived and it is shown that the solution exhibits singular behaviors at multiple nodes due to the initial singularity and time delay. This results in the numerical schemes for solving the equation typically have a lower order of convergence in time. The problem is approximated in time by the L1 and Alikhanov schemes on symmetrical graded meshes, while in space the standard finite element method is applied. Numerical stability and convergence are presented for the schemes. Numerical experiments are performed to show the effectiveness of the schemes.

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二维多项式分数延迟扩散方程的 L1-FEM 离散化

研究考虑了一个二维多项式分数延迟扩散方程。推导出了方程精确解的表示方法，并证明由于初始奇异性和时间延迟，解在多个节点处表现出奇异行为。这导致求解该方程的数值方案在时间上通常具有较低的收敛阶数。该问题在时间上采用对称分级网格上的 L1 和 Alikhanov 方案进行近似，在空间上则采用标准有限元方法。介绍了这些方案的数值稳定性和收敛性。还进行了数值实验，以显示这些方案的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.