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solving ordinary differential equations?

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solving ordinary differential equations?

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arildno

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Although 2. and 3.order Runge-Kutta are quicker than 4th order, they are much less exact.

For orders higher than 4, those take too long time to compute.

On another note:

Although I won't vouch for at which order this will become significant, the upper limit of an approximate scheme in terms of exactness will be when the finite arithmetic of the computer starts messing with the answers we want.

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due to greater accuracy ,the 4th order(RK) method is chosen.

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I agree with you. Just that I never see RK3 formula in the literatures . Why is that so?

Although 2. and 3.order Runge-Kutta are quicker than 4th order, they are much less exact.

For orders higher than 4, those take too long time to compute.

On another note:

Although I won't vouch for at which order this will become significant, the upper limit of an approximate scheme in terms of exactness will be when the finite arithmetic of the computer starts messing with the answers we want.

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arildno

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Probably because R-K increases by two steps of accuracy each time.I agree with you. Just that I never see RK3 formula in the literatures . Why is that so?

It's been a long time since I had a glancing look at the procedure, and have forgotten if 3.order r-k is even possible.

What I remember is that r-k approximates changes due to the values of the derivatives by clever weighting of function values, using a nesting principle.

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