I have read some papers where they say they are using a computational approach to modeling something complicated, like a simplified stock market or something, and they usually say that one of the reasons they are using a computational approach is becuase it would be "very difficult" to come up with a some differential equations to do the same thing. This seems to imply that it would be possible to come up with a set of differential equations which could perform the same function as a agent based computer simulation. Is this actually possible? And, if it is possible to model something as complex as the behavior of a stock market using differential equations, then it seems that it would be possible to model pretty much anything using differential equations. This kind of makes sense to me because another thing I understand is that differential equations are like continuous versions of difference equations. And difference equations can describe all kinds of iterative proccesses, because difference equations are kind of like writing a loop in a computer program which repeatedly changes some intial value according to some rule. Now, since it is possible to write a simulation of some physical system using this same principal (some intial value is repeatedly evalueated according to some rule or interaction of rules), then it should be possible to model this proccess using a difference equation, and it should be possible turn the difference equation into a differential equation. Thus, it should be possible to model anything with a differential equation. Is this correct?