ode2_RK4 - Suppose that we are given a differential...

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Unformatted text preview: Suppose that we are given a differential equation x (t) = f (t, x(t), x (t)), t ∈ [a, b] with x(a) = x0 , x (a) = x0 . Show that Runge-Kutta method (RK4) can be applied to this problem in the following form: h x(t + h) = x(t) + hx (t) + (K1 + K2 + K3 ), 6 1 x (t + h) = x (t) + (K1 + 2K2 + 2K3 + K4 ), 6 where K1 = h · f (t, x(t), x (t)), h h 1 K2 = h · f (t + , x(t) + x (t), x (t) + K1 ), 2 2 2 h h h 1 K3 = h · f (t + , x(t) + x (t) + K1 , x (t) + K2 ), 2 2 4 2 h K4 = h · f (t + h, x(t) + hx (t) + K2 , x (t) + K3 ). 2 (Xin Li, September 22, 2011) 1 ...
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