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### #ActualNightCreature83

Posted 09 January 2013 - 05:07 AM

Runge kutta and euler are methods to approximate of the change in a function over a given time span, and they use different forms of approximation. Euler is very straight forward and just calculates the change over the time span you are interested in and aplies this to the previously calculated values. As you can see this will verge away from the actual value fairly quickly. Runge Kutta is a method of doing this that increases the accuracy of this approximation. The bigger the time span the bigger the values you calculate and thus the bigger the steps you are making in your simulation, which leads to bigger errors. This is why you simulate with a small timestep say 0.01 seconds and then run your simulation for however long it took to update from the last frame. This way the errors in your simulation are a known and you can take these into account when doing collision response or what ever you were trying to approximate. Also it gives you a fixed sample rate on the function instead of a variable one which is what you get if you just pass in the actual elapsed time since the last simulation.

### #1NightCreature83

Posted 09 January 2013 - 05:02 AM

Runge kutta and euler are methods to approximate of the change in a function over a given time span, and they use different forms of approximation. Euler is very straight forward and just calculates the change over the time span you are interested in and aplies this to the previously calculated values. As you can see this will verge away from the actual value fairly quickly. Runge Kutta is a method of doing this that increases the accuracy of this approximation.

The bigger the time span the bigger the values you calculate and thus the bigger the steps you are making in your simulation, which leads to bigger errors. This is why you simulate with a small timestep say 0.01 seconds and then run your simulation for however long it took to update from the last frame. This way the errors in your simulation are a known and you can take these into account when doing collision response or what ever you were trying to approximate.

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