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Euler’s method Consider the initial-value problem y? = ?2y, y(0) = 1. The analytic solution is y(x)...

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Advance Math

Euler’s method

Consider the initial-value problem y? = ?2y, y(0) = 1. Theanalytic solution is y(x) = e?2x . (a) Approximate y(0.1) using onestep of Euler’s method. (b) Find a bound for the local truncationerror in y1 . (c) Compare the error in y1 with your error bound.(d) Approximate y(0.1) using two steps of Euler’s method. (e)Verify that the global truncation error for Euler’s method is O(h)by comparing the errors in parts (a) and (d).

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