Show that the difference method w0 , wi 1 wi a1f (ti ,wi) a2f (ti 2,w1 2f (ti ,wi)), For each i 0, 1 N 1, cannot have local truncation error O (h3) for any choice of constants a1, a2, 2, and 2

Question: Show that the difference method w0 = , wi+1 = wi + a1f (ti ,wi) + a2f (ti + 2,w1 + 2f (ti ,wi)), For

Show that the difference method
w0 = α,
wi+1 = wi + a1f (ti ,wi) + a2f (ti + α2,w1 + δ2f (ti ,wi)),
For each i = 0, 1. . . N − 1, cannot have local truncation error O (h3) for any choice of constants a1, a2, α2, and δ2

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