While going over problems in differential equations and difference equations, I realized that most of the techniques that we use to solve them are very similar. This has led me to wonder - is there a deeper theory that unifies both of them?

I tried to look around, and all that I could find is something called Time-Scale Calculus. How successful is this theory, and are there any other theories that try to unify Differential and Difference Equations?

(PS: By successful, I mean that whether it has been able to explain why exactly Difference and Differential Equations have similar methods of solving them, and also what exactly differentiates them)


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