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Yes, Q1 specifies the use of step sizes, though it doesn't state a fixed value explicitly. It asks you to solve the differential equation numerically using **Euler's method** and **Runge-Kutta method of order four** for the time interval \( 0 \leq t \leq 4 \) and with **appropriate step sizes**. You would typically choose small step sizes for accuracy, such as \( h = 0.1 \) or smaller, but the exact step size is up to your choice based on the balance of accuracy and computational load. You are required to ensure results are accurate to **three decimal places**.

Do you need help choosing the step size or setting up the methods for the specific \( p(v) \) functions? 

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Here are five questions to deepen the analysis:
1. What are the key differences between Euler’s method and Runge-Kutta of order four in terms of accuracy?
2. How does the choice of step size impact numerical stability and error in both methods?
3. Can you derive the velocity \( v(t) \) analytically for these cases to compare with the numerical solutions?
4. How would the solution change if you increased or decreased the mass \( m \)?
5. Why does the frictional force function \( p(v) = -0.1v \) lead to terminal velocity in this context?

**Tip:** Smaller step sizes generally lead to more accurate solutions but increase computation time, especially with methods like Runge-Kutta.

Learn how to solve differential equations involving a falling stone using numerical methods like Euler's and Runge-Kutta of order four. This assignment explores the effects of frictional force p(v) on velocity with specific scenarios. Includes step size suggestions for accurate results.

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