Practice How Rk4 Works (4.3.2) - Numerical Solutions of Ordinary Differential Equations

Practice: How RK4 Works

Lesson 4.3.2Numerical Solutions of Ordinary Differential Equations

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8 questions

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6 sample questions

Question 1.
Define the fourth-order Runge-Kutta method.
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What are the four intermediate values called in RK4?
Question 2.
What is the formula for calculating $k_1$ ?
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Think about the function evaluated at the current time and step size.
3Question 3.
Which of the following steps is not involved in the RK4 method?
- Computing \$ k_1 \$
- Computing \$ k_5 \$
- Computing \$ k_4 \$
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Recall how many intermediate slopes we calculate.
4Question 4.
True or False: RK4 is computationally less expensive than Euler's method.
- True
- False
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Consider the number of calculations involved.
Question 5.
Consider the ODE $\frac{dy}{dt} = y^2$ with $y(0) = 1$ and $h = 0.1$ . Compute the first three approximations using RK4.
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Start with each slope and ensure you use the previous slopes to make adjustments.
Question 6.
Discuss the effects of varying the step size $h$ on the accuracy of RK4. What might happen if you make $h$ too large?
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Consider how the step size impacts the function sampling.

4 more questions in this section. Enroll free to practise them all.