Index reduction for differential-algebraic equations by minimal extension

Index reduction for differential-algebraic equations by minimal extension

In this paper a new index reduction technique is discussed for the treatment of differential-algebraic systems for which extra structural information is available. Based on this information reduced derivative arrays are formed and instead of using expensive subspace computations the index reduction is obtained by introducing new variables. The new approach is demonstrated for several important ...

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...

Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives

Reduction methods for quasilinear differential-algebraic equations

Geometric reduction methods for differential-algebraic equations (DAEs) aim at an iterative reduction of the problem to an explicit ODE on a lower-dimensional submanifold of the so-called semistate space. This approach usually relies on certain algebraic (typically constant-rank) conditions holding at every reduction step. When these conditions are met the DAE is called regular. We discuss in t...

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Index Reduction for Differential-Algebraic Equations by Substitution Method

Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index. In this paper, we p...