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Suppose I have integrated a differential equation numerically using some time-interval $\delta t$.

How might I determine the accuracy of the result? Does solving simultaneous equations reduce the accuracy?

My method is of order 6.

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    It completely depends on both your differential equation and your method of integration. each numerical method comes with explicit estimates, depending on $\delta t$ and your ODE, for example the lipschitz constant of $f$ in $y'=f(y)$. what's your method ?2012-01-12
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    @Glougloubarbaki: Does it suffice to know that the method is of order 6 and the ODE is of the form $\ddot{x}=a(t)x$?2012-01-12
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    if your method is of order 6 then your error is bounded by some $C \delta t^6$, where $C$ is a constant which depends on $a(t)$, the time interval, and the method of integration2012-01-12
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    @Glougloubarbaki: thanks! if i solve the equation by setting simultaneous 1st order odes does that change the order of accuracy of the result generated by my 6th order method?2012-01-12
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    Our sister site [Computational Science](http://scicomp.stackexchange.com) may also be a good place to ask this question.2012-06-20

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