Runge-Kutta vs Euler: Solving Two-Dimensional Differential Equation

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The discussion revolves around solving a two-dimensional differential equation, specifically dx/dt = (-y, x), which describes circular motion. The user initially finds the simple Euler method to be more precise than the fourth-order Runge-Kutta method, leading to frustration and confusion after debugging their code for two days. They question whether there are scenarios where Runge-Kutta performs worse than Euler or if their implementation contains an error. Ultimately, the user discovers a mistake related to an extra time increment in their code, resolving the issue. This highlights the importance of careful coding and debugging in numerical methods.
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Hi, I don't know if this is the right forum to adress, but I will try nevertheless
Im solving a simple two-dimensional differential equation:

dx/dt = (-y,x)

which will give a circle when integrating over time.

Now, the problem is that the simple euler scheme seems to be a lot more precise than the runge-kutta fourth order method. I've spend two whole days trying to debug my code and I feel stuck. so, are there some special cases where rk is worse than euler -- or is there no other explanation than I have made a mistake somewhere (it's four lines of code and my supervisors have had a look without the error popping up.)
 
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great monday... just after complaining in here i found that I've messed an extra time-increment in somewhere in the code :p sorry for the inconvenience
 

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