Global Error

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We know what the one step error is from Accuracy of the Forward (Explicit) Euler Method, which is the error we accumulate in one step. Therefore the global error, which is the error accumulated over all steps, is proportional to

$$N\Delta t^2\propto \frac{T}{\Delta t}\Delta t^2\propto \Delta t$$

Where $N=\frac{T}{\Delta t}$

• This means that the one-step error has an order of 2 - $ϵ\propto \Delta t^2$
• Global error has an order of 1 - $ϵ\propto \Delta t$

We want the order to be as high as possible, due to $\Delta t\ll 1$.