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关键词： Time dependent problem   Semidiscrete formulation   Fully discrete formulation   Mortar mixed method   Elliptic projection   Error analysis  

摘要： We developed and analyzed the multiblock mortar expanded mixed method for second order parabolic partial differential equations. This is a domain decomposition method in which the computational domain is expressed as the union of non-overlapping subdomains separated by interfaces. An auxiliary variable is introduced on the interface which represents the pressure and serves as Dirichlet boundary condition for local subdomain problems. The interface variable also plays the part of Lagrange multiplier to enforce flux matching condition on the interfaces. We explored the expanded mixed method to discretize each subdomain. We propose the semi-discrete formulation and address the solvability of the discrete problem. The optimal order convergence is provided for the continuous time case. We also investigate the fully discrete formulation and derived corresponding error estimates. The numerical experiments are conducted to demonstrate the theory developed in the paper.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Fractional integro-differential equations   Damped system   Controllability   Mittag-Leffler function   Grammian matrix  

摘要： We study the controllability criteria for a class of fractional integro-differential damped systems with impulsive perturbations. The solution representation is derived for both linear and non-linear damped systems, and the introduced formulations were constructed by employing Laplace transformation with Mittag-Leffler matrix function. We present necessary and sufficient conditions for the indicated systems to be controllable in finite dimensional spaces. Here, controllability conditions are proposed by using Grammian matrix as a powerful tool. Two numerical examples are also given at end to demonstrate the obtained theory. (c) 2022 Elsevier B.V. All rights reserved.

关键词： 以学为中心   导数   偏导数   微分方程  

摘要： 基于“以学为中心”的教学理念,本文探究两个函数积、商的导数(或偏导数)等于其导数(或偏导数)积、商的问题,给出了此结论成立的非平凡实例.

关键词： 并网变流器   数字控制延时   稳定性   一阶微分  

摘要： 数字控制系统中的延时对并网变流器的稳定性有着重要影响,因此在建立并网变流器数学模型的基础上,根据Nyquist判据分析了延时环节对系统稳定性的影响。针对延时环节易导致系统不稳定的问题,基于零极点对消原理提出了一种基于一阶微分的并网变流器控制策略,分析结果表明该方法可削弱控制延时对系统稳定性的不利影响,显著提高系统的稳定性。最后通过仿真和实验验证了一阶微分控制策略的有效性。