Model discretization by the FDA (§7.3.1) and bilinear transform (§7.3.2) methods are order preserving. As a result, they suffer from significant approximation error, especially at high frequencies relative to half the sampling rate. By allowing a larger order in the digital model, we may obtain arbitrarily accurate transfer-function models of LTI subsystems, as discussed in Chapter 8. Of course, in higher-order approximations, the state variables of the simulation no longer have a direct physical intepretation, and this can have implications, particularly when trying to extend to the nonlinear case. The benefits of a physical interpretation should not be given up lightly. For example, one may consider oversampling in place of going to higher-order element approximations.
General Nonlinear ODE
Application of the Bilinear Transform