Numerical simulation of systems of differential equations is made by the ode primitive. Many solvers are available, mostly from odepack, for solving stiff or non-stiff systems. Implicit systems can be solved by dassl. It is also possible to solve systems with stopping time: integration is performed until the state is crossing a given surface. See ode and dassrt commands. There is a number of optional arguments available for solving ode's (tolerance parameters, jacobian, order of approximation, time steps etc). For ode solvers, these parameters are set by the global variable %ODEOPTIONS.
Minimizing non linear functions is done the optim function. Several algorithms (including non differentiable optimization) are available. Codes are from INRIA's modulopt library. Enter help optim for more a more detailed description.