High Performance Algorithms for Computing Nonsingular Jacobian-Free Piecewise Linearization of Differential Algebraic Equations

Abstract

Numerical methods for solving differential algebraic equations (DAEs) have received considerable attention in recent years. Most of the available numerical methods are based on the approximation of a continuous model by a discrete model, and the computation of an approximate solution in a finite set of points. In the present work an extension of the methodology presented in [1] to consider the following differential algebraic equation (DAE) problem has been carried out:

$$ M\dot x(t) = f(x(t),t), x(t_0 ) = x_0 $$

where M ∈ R ^N×N, x(t) ∈ R ^N, t ∈ R, f is a continuous Lipschitzian function on the domain Ω ∁ R ^N × R.