Derivation of a fourth-order Co-simulation method for linear systems

In this article, we present a detailed derivation of a fourth order co-simulation method. This method is implicit and based on Hermite extrapolation with two support points and their derivatives. The convergence order of the local and global errors is analyzed and tested on two linear systems from the mechanical and the electrical fields. Both systems are decomposed into two subsystems to perform co-simulation. We compare the fourth-order method with lower-order methods, confirming the expected convergence of the local error and showing that the global error of the derived method corresponds to O(H4).