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Using the form y' = f ( t,y ) to write differential equation, also assuming we know the initial condition y ( to ) = you 7 Our objective is to approximate the value of y at time t= to 7 We select a step -size of time, which we'll represent by h. Starting at time += 0 , our strategy will be to move forward one step at a time , solving for the "approximate value of the function y ( + ) at that time step , then using that most recent approximation as the basis for taking next step. - To state the algorithm in its most general form, define time step n+1 as -> Tate = tath -7 Un + 1 = yn + To ( k, + 2 kz + 2k3 + Ky) -7 K, = f ( t + ym ) an=0 s to+1 =toth K2 = f ( tn+zi un+ 2 to = 0 K, = f ( t , , Un ) K3 = f ( tn +2 , un+ 2 y (to ) = yo K2 = f ( tn+ 2 3 4n + 2 Ky = f ( t n th , Un + K3 ) to