Simultaneous Numerical Solution of Differential-Algebraic Equations

Numerical Solution of Differential Algebraic Equations

Numerical Solution of Hybrid Systems of Differential-algebraic Equations

We present a mathematical framework for general overand underdetermined hybrid (switched) systems of differential-algebraic equations (HDAEs). We give a systematic formulation of HDAEs and discuss existence and uniqueness of solutions, the treatment of the switch points and how to perform consistent initialization at switch points. We show how numerical solution methods for DAEs can be adapted ...

The Numerical Solution of Delay-differential-algebraic Equations of Retarded

In this paper we consider the numerical solution of initial-value delay-differentialalgebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well conditioned and show how the DDAE is related to an underlying retarded or neutral delay-ordinary differential equation (DODE). We present convergen...

Numerical solution of differential-algebraic equations in mechanical systems simulation

The numerical solution of the differential-algebraic equations of motion of mechanical systems offers many computational challenges. In this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability, and outline some of the difficulties which must be resolved for efficient and reliable numerical methods i...

Hybrid systems of differential-algebraic equations – Analysis and numerical solution

We consider hybrid systems of differential-algebraic equations and present a general framework for general nonlinear overand underdetermined hybrid systems that allows the analysis of existence and uniqueness and the application of index reduction methods for hybrid differential-algebraic systems. A particular difficulty in the numerical simulation of hybrid systems is (numerical) chattering, i...