Question

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?

Answer 1

The answer is "13".

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> (\log(0.000000001) )/(\log(0.2)) \\\\ \to 12.876 \approx 13`