Practice The Fourth-order Runge-kutta Method (rk4) (4.3.1) - Numerical Solutions of Ordinary Differential Equations

Practice: The Fourth-Order Runge-Kutta Method (RK4)

Lesson 4.3.1Numerical Solutions of Ordinary Differential Equations

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define the Fourth-Order Runge-Kutta Method.
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Think about what makes it different from simpler methods.
Question 2.
What is k1 in the RK4 formula?
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Remember, it uses the function f evaluated at initial conditions.
3Question 3.
What is the main advantage of the RK4 method over Euler's method?
- Higher accuracy
- Lower computational cost
- Simplicity
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Think about how accuracy is derived in each method.
4Question 4.
Is RK4 suitable for solving stiff equations?
- True
- False
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Recall the characteristics of stiff equations.
Question 5.
Given the initial value problem dy/dt = -2y with the initial condition y(0) = 1, calculate y(0.2) using RK4 with h = 0.1.
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Work through step-by-step as RK4 requires computed intermediate values.
Question 6.
For the ODE dy/dt = 3t^2 + 2y, find y(1) with y(0) = 1 using h = 0.1 and RK4.
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Recall how to apply the RK4 method at each interval based on your previous calculations.

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