RK4 - n K 2 = Δ tf t n Δ t 2,u n K 1 2 K 3 = Δ tf t n Δ...

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CS 111 - Introduction to Computational Science Fourth Order Accurate Runge-Kutta Scheme Consider the following ODE: ± du dt = f ( u,t ) u (0) = u 0 , where u 0 is the given initial data. Then RK4 is written as: K 1 = Δ tf ( t n ,u
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Unformatted text preview: n ) K 2 = Δ tf ( t n + Δ t 2 ,u n + K 1 2 ) K 3 = Δ tf ( t n + Δ t 2 ,u n + K 2 2 ) K 4 = Δ tf ( t n + Δ t,u n + K 3 ) u n +1 = u n + K 1 6 + K 2 3 + K 3 3 + K 4 6 1...
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