广义时间分数型Burgers方程的二阶格式

IF 1.9 4区工程技术 Q3 ENGINEERING, MECHANICAL

Journal of Computational and Nonlinear Dynamics Pub Date : 2023-10-16 DOI:10.1115/1.4063792

Reetika Chawla, Devendra Kumar, Satpal Singh

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引用次数: 0

摘要

提出了一种求解广义时间分数型Burgers方程的二阶数值格式。在卡普托意义上考虑时间分数阶导数。首先，采用拟线性化方法对时间分数型Burgers′进行线性化处理;方程，给出了一系列线性偏微分方程(PDEs)。采用Crank-Nicolson格式对时间方向上的偏微分方程序列进行离散化，然后给出一阶和二阶空间导数的中心差分公式。通过细致的理论分析得到了建立的误差界(在L^2-$范数内)，表明该方法在空间和时间上都是二阶收敛的。该技术也被证明是有条件稳定的。通过数值实验验证了理论结果。

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A Second-order Scheme for the Generalized Time-fractional Burgers' Equation

Abstract A second-order numerical scheme is proposed to solve the generalized time-fractional Burgers' equation. Time-fractional derivative is considered in the Caputo sense. First, the quasilinearization process is used to linearize the time-fractional Burgers'; equation, which gives a sequence of linear partial differential equations (PDEs). The Crank-Nicolson scheme is used to discretize the sequence of PDEs in the temporal direction, followed by the central difference formulae for both the first and second-order spatial derivatives. The established error bounds (in the $L^2-$norm) obtained through the meticulous theoretical analysis show that the method is the second-order convergent in both space and time. The technique is also shown to be conditionally stable. Some numerical experiments are presented to confirm the theoretical results.

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来源期刊

Journal of Computational and Nonlinear Dynamics 工程技术-工程：机械

CiteScore

4.00

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.