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 August 7th, 2019, 03:47 AM #1 Newbie   Joined: Aug 2019 From: Australia Posts: 2 Thanks: 0 Differential equation assignment Problem 2: Consider the following Initial Value Problem (IVP) where (𝑡) is the dependent function: 𝑦 ′ = 𝑦 − 𝑦 2 + 1.14 cos(𝑒 𝑡/2 ) with 𝑦(0) = 𝑦0 and 𝑡 ≥ 0 Approximate the solution to the IVP using the RK4 method with the following conditions: Initial condition 𝑦0 = 1; time steps ℎ = 1 8 , 1 16 , 1 32 , 1 64 ; and time interval 𝑡 ∈ [0,20] Plot the RK4 approximation for all 4 time steps Discuss the results of these approximations
 August 7th, 2019, 05:45 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 Is the equation below what you intended? $y' = y - y^2 + 1.14\cos\left(e^{t/2}\right)$ with $y(0) = y_0$ and $t \geqslant 0$
 August 7th, 2019, 05:49 AM #3 Senior Member   Joined: Jun 2019 From: USA Posts: 120 Thanks: 40 Runge-Kutta is pretty cut and dry. What part are you having trouble with, exactly?
 August 7th, 2019, 08:35 AM #4 Newbie   Joined: Aug 2019 From: Australia Posts: 2 Thanks: 0 yes,I meant it
 August 7th, 2019, 09:19 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 The RK4 method is described here.

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