Assume that the solution y(t) to the equation y'(t...



Show transcribed image text Assume that the solution y(t) to the equation y'(t) = f(t, y(t)) is a 3rd order polynomial. Show two step Adams - Bash forth method has the local truncation error given as follows for some constant: eta B: LB(y, h, tn) = 1/h(1/2!y3(eta B) (t - tn)(t - tn - 1)dt). Show that one step Adams - Moulton method has the following local truncation error for some constant eta M: LM(y, h, tn) = 1/h(1/2!y3(eta M) (t - tn + 1) (t - tn)dt). Can you deduce that one step Adams - Moulton method is better than two step Adams - Bash ford method based on these facts? If so, why ?
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