Consider the strategy we introduced about adaptive error control which uses two different methods of different order with the

Question

Consider the strategy we introduced about adaptive error control which uses two different methods of different order with the same step size Assume we use Euler s method to get w and midpoint rule to get u to approximate y that solves y y t 1 with y 0 0 5 and h 1 simultaneously a Compute w and by the two methods b Assuming the desired local truncation error is 0 1 compute the largest q so that qh for Euler s method can approximately ensure that the local truncation error is smaller than 0 1 Point out whether the current step size is acceptable or not You do not need to consider the case that there is an extra factor 2 in the definition of q hint recall the expression for q in Lec 7 and choose n 1

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