This is an extract from my third year notes on 'Computational Physics':(adsbygoogle = window.adsbygoogle || []).push({});

The Euler method is inaccurate because it uses the gradient evaluated at the initial point to

calculate the next point. This only gives a good estimate if the function is linear since the truncation error is quadratic in the step size.

My question is this:

If the function is linear, then the Euler method must give the exact answer as the gradient lies on the line. So, why does it say that the Euler method only gives a good estimate if the function is linear.

Any ideas? Is it wrong?

Should it be the Euler method only gives a good estimate if the function isapproximatelylinear, so that the quadratic and higher order terms of the function in that case are much much smaller than the linear term so that the error is minimal?

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# Euler method question

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