Index-Aware Model-Order Reduction for a Special Class of Nonlinear Differential-Algebraic Equations

Model Reduction of Nonlinear Differential-algebraic Equations

∗ Division of Automatic Control Department of Electrical Engineering, Linköpings universitet, SE-581 83 Linköping, Sweden ∗∗ Department of Mechanical Science and Engineering, Nagoya University, Japan Abstract: In this work, a computational method to compute balanced realizations for nonlinear differential-algebraic equation systems is derived. The work is a generalization of an earlier work for...

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...

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

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 ...

The variational iteration method for a class of tenth-order boundary value differential equations