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August 7th, 2019, 03:47 AM   #1
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Differential equation assignment

Problem 2: Consider the following Initial Value Problem (IVP) where (𝑑) is the dependent function:
𝑦 β€² = 𝑦 βˆ’ 𝑦 2 + 1.14 cos(𝑒 𝑑/2 ) with 𝑦(0) = 𝑦0 and 𝑑 β‰₯ 0
Approximate the solution to the IVP using the RK4 method with the following conditions:
Initial condition 𝑦0 = 1;
time steps β„Ž = 1 8 , 1 16 , 1 32 , 1 64 ; and time interval 𝑑 ∈ [0,20]
Plot the RK4 approximation for all 4 time steps
Discuss the results of these approximations
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August 7th, 2019, 05:45 AM   #2
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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 $t \geqslant 0$
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August 7th, 2019, 05:49 AM   #3
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Runge-Kutta is pretty cut and dry. What part are you having trouble with, exactly?
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August 7th, 2019, 08:35 AM   #4
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yes,I meant it
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August 7th, 2019, 09:19 AM   #5
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The RK4 method is described here.
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