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In general in a correctly implemented fixed-step ODE solver method you have 3 sources for numerical errors: the theoretical method truncation error, the floating point error from evaluating the ODE function and composing the method step and the error from accumulating the single updates of size $O(h)$ to the integration result of size $O(1)$. So the total ...


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I can share my perspective on this topic and can try to prove that the Leapfrog (velocity Verlet) is time-reversible, according to an appropriate definition of time reversibility (very nice property that increases this integration method's accuracy, alongside its $\Delta t^2$ convergence and symplecticity). The idea behind Leapfrog: Assume you have a system ...


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