First, we present a general convergence result for a co-simulation of Gauß-Seidel and of Jacobi type for coupled DAEs of the form \[\begin{aligned} f_1(\frac{\operatorname{d}}{\operatorname{d}\!t} m_1(x_1,t), x_1, g_2(x_2), t)&= 0,\\ f_2(\frac{\operatorname{d}}{\operatorname{d}\!t} m_2(x_2,t), x_2, g_1(x_1), t)&= 0. \end{aligned}\] Both DAEs may have a higher index but the perturbation index of the systems \[\begin{aligned} f_i(\frac{\operatorname{d}}{\operatorname{d}\!t} m_i(x_i,t), x_i, \delta_i, t)&= 0 \end{aligned}\] is assumed to be not larger than 1 for perturbations \(\delta_i\) and \(i\in\{1,2\}\). Note that the perturbations \(\delta_i\) reflect only perturbations at the interface between both DAE systems. We demonstrate how the convergence rate can be influenced by the interplay of the interface functions \(g_1\) and \(g_2\) with the DAE model functions \(f_1\) and \(f_2\).

In the second part, we discuss particular DAE models for flow networks (circuits, energy systems, networks of neurons) and provide network topological convergence criteria for the co-simulation.