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

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SUMMARY

The discussion centers on the comparison between the Euler method and the Runge-Kutta fourth order method for solving a two-dimensional differential equation, specifically dx/dt = (-y, x). The user initially observed that the Euler scheme appeared to yield more precise results than the Runge-Kutta method. After debugging, the user discovered an error related to an extra time increment in their code, which clarified the discrepancy in performance between the two methods.

PREREQUISITES
  • Understanding of differential equations, particularly two-dimensional systems.
  • Familiarity with numerical methods for solving differential equations, specifically Euler and Runge-Kutta methods.
  • Proficiency in a programming language suitable for implementing numerical algorithms (e.g., Python, MATLAB).
  • Basic knowledge of debugging techniques in coding.
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  • Research the implementation details of the Runge-Kutta fourth order method.
  • Explore error analysis in numerical methods to understand precision differences.
  • Learn about adaptive step size methods to improve numerical integration accuracy.
  • Investigate common pitfalls in coding numerical algorithms and debugging strategies.
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Mathematicians, engineers, and computer scientists involved in numerical analysis, particularly those working with differential equations and numerical methods for simulations.

mrsvan
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Hi, I don't know if this is the right forum to address, 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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