(1) Consider a two stage Runge Kutta method ki = f(xk,Yk) k2 = f(xx +ah,yŁ+ ahk|) Yk+1 = yk +h(cıkı +c2k2) (a). What are the conditions for the three parameter a,c¡ and c2 that the method has maxi- mum order? (b). Show that the order can not exceed two, and hence derive the Midpoint's Method.

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