电容电路
安萨茨
数学
摄动(天文学)
代数数
边值问题
线性系统
应用数学
时域
数学分析
拓扑(电路)
控制理论(社会学)
计算机科学
物理
组合数学
电压
电容器
控制(管理)
量子力学
人工智能
数学物理
计算机视觉
标识
DOI:10.1076/mcmd.7.2.189.3649
摘要
Abstract In electrical circuit simulation, a refined generalized network approach is used to describe secondary and parasitic effects of interconnected networks. Restricting our investigations to linear RLC circuits, this ansatz yields linear initial-boundary value problems of mixed partial-differential and differential-algebraic equations, so-called PDAE systems. If the network fulfils some topological conditions, this system is well-posed and has perturbation index 1 only: the solution of a slightly perturbed system does not depend on derivatives of the perturbations. As method-of-lines applications are often used to embed PDAE models into time-domain network analysis packages, it is reasonable to demand that the analytical properties of the approximate DAE system obtained after semidiscretization are consistent with the original PDAE system. Especially, both should show the same sensitivity with respect to initial and boundary data. We will learn, however, that semidiscretization may act like a deregularization of an index-1 PDAE model, if an inappropriate type of semidiscretization is used.
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