Related papers: Index Reduction for Differential-Algebraic Equatio…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely…
Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…
Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…
Integro-differential-algebraic equations (IDAE)s are widely used in applications of engineering and analysis. When there are hidden constraints in an IDAE, structural analysis is necessary. But if derivatives of dependent variables appear…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAE), i.e., constraints of the form f(dot{x},x,u)=0. This drastically facilitates modeling from first…
We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for…
Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
This paper deals with the structural analysis problem of dynamic lumped process high-index DAE models. We consider two methods for index reduction of such models by differentiation: Pryce's method and the symbolic differential elimination…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems…
Differential-algebraic equations (DAEs) have been used in modeling various dynamical systems in science and engineering. Several preprocessing methods for DAEs, such as consistent initialization and index reduction, use structural…
In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs).…
The definition of index for differential algebraic equations (DAEs) or integral algebraic equations (IAEs) in the linear case (time variable) depends only on the coefficients of integrals or differential operators and the coefficients of…
Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which…