Practice Rk4 Example (4.3.4) - Numerical Solutions of Ordinary Differential Equations

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6 sample questions

Question 1.
What is the step size used in the RK4 example?
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Look at the example step size mentioned.
Question 2.
How many k-values are computed in the RK4 method?
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Recall the number of slopes we use in RK4 to enhance accuracy.
3Question 3.
What is the formula to compute k1 in the RK4 method?
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Think about the relationship between the function and its derivative.
4Question 4.
True or False: The RK4 method is less accurate than Euler's method.
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Consider what additional calculations RK4 performs.
Question 5.
Given the ODE dy/dt = -2y with y(0) = 1 and h = 0.1, compute the first two steps using the RK4 method.
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Remember to apply the RK4 formula for each slope!
Question 6.
How would increasing the step size to h = 0.5 affect the outcome of the RK4 approximation for dy/dt = y?
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Think about how RK4 approximates the curve of the function.

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