Is recursion a type of differential equations Unfortunately, this question has a very bland answer; however, it occurred to me that recursive functions, like ones to program and calculate factorials for instance, are very similar to differential equations whose results depend on initial conditions. Is recursion essentially just discrete DEs, versus the typical continuous DEs learned at school?

Discrete Differential equations are called "Difference Equations" and are mostly expressed by $$k_{n+1} - k_{n} = f(n, k) \quad n\in \mathbb{N}$$
These give the difference between two consecutive values. 
Recursive Expressions ware mostly stated by $$k_{n+1} = f(n, k)$$ It is always possible to make this into a difference equation by just subtracting $k_n$ on both sides though. 
