Example

The acausal bond graph of system ImplicitRC is displayed in Figure 2.1 (on page ) and its label file is listed in Section 2.1.3 (on page ) The subsystems are listed in Section 2.1.4 (on page ).

The system represents two simple RC circuits in series with differential equations as given in Section 2.3 (on page ) and transfer function as given in Section 2.6 (on page ).

For the purposes of this example the two time constants are $1$ and $\epsilon=10^{-3}$ - this is a stiff system. All of the simulations use a sample interval of $\Delta t = 0.1$ ang the input is a unit step. Section 2.7 (on page ) shows the exact (computed from the matrix exponential) solution, and Section sec:ImplicitRC_odeso-cc.ps shows the solution by implicit integration.

The explicit solution is not shown, but was found to be unstable for $\Delta t > 0.002$ as predicted.