Parallel Treatment of a Class of Differential-Algebraic Systems

Abstract

In this paper we derive an asynchronous method for the parallel solution of a class of index-one differential-algebraic systems with initial values. These systems are in the form \[ \left\{ \begin{gathered} f(x'(t),x(t),y(t),t) = 0, \hfill \\ g(x(t),y(t),t) = 0, \hfill \\ x\left( {t_0 } \right)x_0 . \hfill \\ \end{gathered} \right. \]$g(x,y,t) = 0$ must be solvable with respect to y. This study allows us to give asynchronous extensions of the waveform relaxation method.