McSimAPN does it all!
McSimAPN is made to work rather like an (electronic) ANALOGUE COMPUTER . Blocks are connected together to mimic the real world prototype. With a major added facility: it will simulate discrete event processes using the concepts of PETRI NETS to provide a simulation tool that has the discrete event modelling and the continuous systems modelling in one seamless combination. Well, that's the idea anyway. There are limits, of course and big complex problems may need more powerful tools, but seeing how simple the model can be and still provide insight is an important first step.
McSimAPN stands for "McCannScience Simulator for Analogue and Petri-Nets" because it is like an analogue computer that does Petri Nets as well.

Differential Equations.
Part of McSimAPN requires integration. Over centuries, a lot of work has gone into getting near perfect numerical solutions to differential equations.
In McSimAPN, I have used the simpest possible, Euler integration method, because here the objective is a working model of a real world prototype, not ultimate precision in the solution of a set of differential equations.
Computational errors due to the crude integration can be reduced by finer resolution and, anyway, so long as the model doesn't become computationally unstable, all numerical integration schemes are conservative (in the sense of conservation of energy, momentum,mass) and the errors can be reduced below the level due to uncertainty in the model parameters.
Critically for this tool, using a discrete time stepping method allows a merger of discrete events with continous processes which needs special procedures in other methods such as Runge-Kutta.
McSimAPN does allow time-step size to change without breaking the model.

Event Chains, Discrete Events and Petri-Nets.
Some of the most powerful discrete event simulation tools are based on set-theoretic concepts and use event chains to handle the calling of routines (which in many cases have to be written specially by the user) to calculate the consequences of an event and to set the conditions for the next event. The event chain is the sorted list of forthcoming events.
The events result in state changes, set membership changes and the setting of times for some subsequent events that then get listed in the event chain.
These powerful tools can deal with each item or token, that moves around from one set to another, carrying its own history and parameters so that each time it is operated on that data can determine what happens next.

A different formulation uses a PetriNet view of things to do the same sort of operation. Such a schema can be seen as a flow chart in which tokens move around. Transitions move the tokens from one place to another.
In the Petri-Net form used in McSimAPN, each block has an input transition to an internal place where a token stays for a period of time and an exit transition whence the token leaves if it has some place to go.
Each block generally represents some real world object, though it might be a computer programme or procedure.
The tokens in McSimAPN are indistinguishable one from another (they are not "coloured". That's a big simplification, but it turns out that in many systems the place its in really defines the relevant properties and so they don't need to be carried around.
Therefore McSimAPN includes a Timed Monochromatic Petri Net formulation.
McSimAPN does extend the idea of a token. Because the calculations are all done with floating point arithmetic, it becomes possible for the tokens to represent arbitrary sized quantities and to link the movement of tokens to the movement of materials which can be part of the continuous system model.