Practice Numerical Solutions of Ordinary Differential Equations - 4 | 4. Numerical Solutions of Ordinary Differential Equations | Numerical Techniques
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Numerical Solutions of Ordinary Differential Equations

4 - Numerical Solutions of Ordinary Differential Equations

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define an ordinary differential equation (ODE).

💡 Hint: Think about how these equations relate to functions.

Question 2 Easy

What does Euler's method calculate at each step?

💡 Hint: Refer to the Euler's Method formula.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Euler's method use to update the solution?

The last two function values
The last function value and its derivative
Only the last function value

💡 Hint: Think about how derivatives relate to rates of change.

Question 2

True or False: The Runge-Kutta method is less accurate than Euler's method.

True
False

💡 Hint: Have you compared both methods in terms of step calculations?

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Euler's Method, solve the differential equation dydt=3y for y(0)=1 with a step size of h=0.2 for 5 iterations. How does this compare to the actual solution?

💡 Hint: Consider how each step builds on the last.

Challenge 2 Hard

Implement the fourth-order Runge-Kutta method for the same function dydt=3y, y(0)=1, over the same 5 iterations. Compare the RK4 output to the values you obtained from Euler's method.

💡 Hint: Focus on calculating the k values carefully.

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