A nonuniform linearized Galerkin-spectral method for nonlinear fractional pseudo-parabolic equations based on admissible regularities

IF 1.6 4区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC International Journal of Numerical Modelling-Electronic Networks Devices and Fields Pub Date : 2024-04-10 DOI:10.1002/jnm.3233

M. Fardi, S. Mohammadi, A. S. Hendy, M. A. Zaky

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Abstract

In this paper, we deal with the nonlinear fractional pseudo-parabolic equations (FPPEs). We propose an accurate numerical algorithm for solving the aforementioned well-known equation. The problem is discretized in the temporal direction by utilizing a graded mesh linearized scheme and in the spatial direction by the Galerkin-spectral scheme. We investigate the stability conditions of the proposed scheme. We also provide an $H^{1}$ error estimate of the proposed approach to demonstrate that it is convergent with temporal second-order accuracy for fitted grading parameters. The proposed scheme is also extended to tackle coupled FPPEs. Numerical experiments are provided to validate the accuracy and reliability of the proposed scheme.

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基于可允许正则性的非线性分数伪抛物方程的非均匀线性化 Galerkin 频谱方法

本文讨论非线性分数假抛物方程（FPPE）。我们提出了一种精确的数值算法来求解上述著名方程。利用分级网格线性化方案在时间方向上对问题进行离散化，利用 Galerkin 频谱方案在空间方向上对问题进行离散化。我们研究了所提方案的稳定性条件。我们还提供了所提方法的 H 1 $$ {H}^1 $$ 误差估计值，以证明该方法在拟合分级参数时具有时间二阶收敛精度。所提方案还可扩展用于处理耦合 FPPE。数值实验验证了所提方案的准确性和可靠性。

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

International Journal of Numerical Modelling-Electronic Networks Devices and Fields 工程技术-工程：电子与电气

CiteScore

4.60

自引率

6.20%

发文量

101

审稿时长

>12 weeks

期刊介绍： Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models. The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics. Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.