Index Reduction and Discontinuity Handling Using Substitute Equations

Index Reduction and Discontinuity Handling using Substitute Equations

Several techniques exist for index reduction and consistent initialization of higher index DAEs. Many such techniques change the original set of equations by differentiation, substitution, and/or introduction of new variables. This paper introduces substitute equations as a new language element. By means of a substitute equation, the value of a continuous variable or its time derivative is spec...

Substitute Equations for Index Reduction and Discontinuity Handling

Several techniques exist for index reduction and consistent initialization of higher index DAEs. Many such techniques change the original set of equations by differentiation, substitution, and/or introduction of new variables. This paper introduces substitute equations as a new language element. By means of a substitute equation, the value of a continuous variable or its time derivative can be ...

Index Reduction in Differential-Algebraic Equations Using Dummy Derivatives

Discontinuity preserving disparity estimation with occlusion handling

In this paper, we propose a stereo matching algorithm based on distance transform to generate high-quality disparity maps with occlusion handling. In general, pixel intensities around object edges are smeared due to mixed values located between the object and its background. This leads to problems when identifying discontinuous disparities. In order to handle these problems, we present an edge ...

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...