# Runge-Kutta method for ut = f(x,y)?

Hi,

I am trying to solve something similar to ut = f(x,y), and ut = f(t,x,y) using RK4. I asked a few friends, and nobody knew for sure how to go about it. I've also looked online, without much success. Can anyone give me a hint on this one?

In reality, it is probably preferable to derive a scheme from the first principle, but if I could avoid this, that would be nice. Thanks.

Integral
Staff Emeritus
Gold Member
Sorry, I don't understand your notation.

R-K algorithms are for solving differential equations, is that what you have?

Sorry, how about something like the following?

$\frac{du}{dt} = x^2 + sin(y)$

Isn't this solved by using simultaneous RK4's?

I think it's supposed to be u'(t) = f(x,y) and u'(t) = f(t,x,y)? I don't understand the question clearly ^Thanks, I think that is probably what I was looking for!

One bonus question, while we're at it. Is there still value to using the RK method for the differential equation I listed in my previous post? That is, one with f(x,y), rather than f(t,x,y)?

Redbelly98
Staff Emeritus