Question: Show that the fourth-order Runge-Kutta method, k1 = hf (ti ,wi), k2 = hf (ti + h/2,wi + k1/2), k3 = hf (ti + h/2,wi

Show that the fourth-order Runge-Kutta method,
k1 = hf (ti ,wi),
k2 = hf (ti + h/2,wi + k1/2),
k3 = hf (ti + h/2,wi + k2/2),
k4 = hf (ti + h,wi + k3),
wi+1 = wi + 1/6 (k1 + 2k2 + 2k3 + k4),
when applied to the differential equation y' = λy, can be written in the form
wi+1 = (1 + hλ + 1/2 (hλ)2 + 1/6 (hλ)3 + 1/24(hλ)4) wi .

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