Mathematics: If the constant bounding the error in the Euler method is 0.2 and you wanted a 9 decimal place accuracy, how many steps, n, would you need ensure this accuracy?

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If the constant bounding the error in the Euler method

j015

17.04.2021

The answer is "13".

Step-by-step explanation:

Euler method=e=0.2 constantly binding the error

Precision should be 9 decimal places=0.000000001

The number of steps should be n.

In order to guarantee precision,

$\to 0.2^n 0.000000001\\\\ \to n \frac{\log(0.000000001) }{\log(0.2)} \\\\ \to 12.876 \approx 13$

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