Higher-index differential-algebraic equations: analysis and numerical treatment

Least-squares collocation for linear higher-index differential-algebraic equations

Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for linear differential-algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discreti...

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...

Numerical Algebraic Geometry and Differential Equations

In this paper we review applications of numerical algebraic geometry to differential equations. The techniques we address are direct solution, bootstrapping by filtering, and continuation and bifurcation. We review differential equations systems with multiple solutions and bifurcations.

Index reduction of differential algebraic equations by differential algebraic elimination

High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish...

Numerical Solution of Differential Algebraic Equations