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→Integration: Leapfrog is vastly superior to RK Tags: Mobile edit Mobile web edit |
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x.new = x.old + (v.new + v.old) * 0.5 * dt
Of course still better results can be expected by taking intermediate values. This is what happens when using the [[Runge-Kutta]] method, especially the one of grade 4 or 5 are most useful. The most common method used is the [[leapfrog method]] due to its good long term energy conservation.
A completely different method is the use of [[Taylor series]]. In that case we write: <math>r = r_0 + r'_0 t + r''_0 \frac{t^2}{2!} + ... </math>
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