English
Related papers

Related papers: Differential algebraic system nodes

200 papers

In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…

Functional Analysis · Mathematics 2007-05-23 Jorge Antezana , Gustavo Corach , Demetrio Stojanoff

Motivated by recent work in this area we expand on a generalization of port-Hamiltonian systems that is obtained by replacing the Hamiltonian function representing energy storage by a general Lagrangian subspace. This leads to a new class…

Optimization and Control · Mathematics 2018-08-07 Arjan van der Schaft , Bernhard Maschke

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…

Commutative Algebra · Mathematics 2015-05-19 Thomas Bächler , Vladimir Gerdt , Markus Lange-Hegermann , Daniel Robertz

In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…

Computational Engineering, Finance, and Science · Computer Science 2023-04-26 Vladimir Salnikov , Antoine Falaize , Daria Loziienko

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 T. Cerquetelli , N. Ciccoli , M. C. Nucci

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…

High Energy Physics - Theory · Physics 2009-10-30 Artemio Gonzalez-Lopez , Niky Kamran , Peter J. Olver

This paper studies the contraction property of time-varying differential-algebraic equation (DAE) systems by embedding them to higher-dimension ordinary differential equation (ODE) systems. The first result pertains to the equivalence of…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Hao Yin , Bayu Jayawardhana , Stephan Trenn

The aim is to determine the derivations of the three series of finite-dimensional Z-graded Lie superalgebras of Cartan-type over a field of characteristic p > 3, called the special odd Hamiltonian superalgebras. To that end we first…

Representation Theory · Mathematics 2010-07-08 Wei Bai , Wende Liu , Lan Ni

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

Optimization and Control · Mathematics 2023-06-16 Sumit Suthar , Soumyendu Raha

Solutions of nonlinear multi-component Euler-Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem. Nonlocal structures are an essential feature…

Mathematical Physics · Physics 2009-11-07 Thomas Curtright , David Fairlie

This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…

Classical Analysis and ODEs · Mathematics 2020-07-09 Vladimir A. Dorodnitsyn , Roman Kozlov , Sergey V. Meleshko , Pavel Winternitz

The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…

Mathematical Physics · Physics 2009-12-22 M. B. Sedra

This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…

Numerical Analysis · Mathematics 2022-10-05 Idoia Cortes Garcia , Iryna Kulchytska-Ruchka , Sebastian Schöps

Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize…

Category Theory · Mathematics 2007-05-23 Anders Kock , Gonzalo E. Reyes

The abstract elliptic and parabolic equations on exterior domain are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the…

Analysis of PDEs · Mathematics 2017-06-06 Veli Shakhmurov

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

Symbolic Computation · Computer Science 2026-01-14 Louis Gaillard

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

Functional Analysis · Mathematics 2022-03-04 Helge Glockner

Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…

Dynamical Systems · Mathematics 2013-01-16 V. N. Gorbuzov

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

Representation Theory · Mathematics 2015-12-17 Charles H. Conley

A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…

Functional Analysis · Mathematics 2023-02-03 Bálint Farkas , Birgit Jacob , Timo Reis , Merlin Schmitz