# What should applying the Runge-Kutta-method 4 on a differential equation be called?

What should applying the Runge-Kutta-method 4 to a differential equation using a program be called? Does it qualify as "simulation"?

I'm asking because I'm writing a document for school, and now I'm not sure about what should be the title of the section in which I write a program to do RK4 on previously discussed equations and look at the results of putting different parameters into it.

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"applying to", not "applying on". – joriki Mar 6 '12 at 18:36
@joriki: Oh, thanks. – thejh Mar 6 '12 at 20:25
I guess, a numerical analyst would say that he "solved the equation with the RK4 method". – Dirk Mar 6 '12 at 20:36

## 1 Answer

By applying RK4 to an ODE, one solves the equation numerically: that is, a numeric solution is obtained. It is implicitly understood that a numeric solution is a finite vector of floating-point reals, rather than a map from an interval $(a,b)$ to $\mathbb R$; it's a rather different kind of object. Both are called solutions, even though they are not the same. One says numeric solution and exact solution when disambiguation is necessary.

I would not use the word "simulation" for this purpose; it brings to mind simulation of a physical process by something less tangible. In a sense, numerical algorithms do the opposite of that.

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