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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Calculate k1 for the equation dy/dx = 2y with y(0) = 1 and h = 0.1.
💡 Hint: Use the initial value directly in the function.
Question 2
Easy
What is the formula for predicting the next value y* in the Modified Euler’s Method?
💡 Hint: Remember, k1 is the slope at the initial point.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the core improvement of Modified Euler's Method over standard Euler's Method?
- It uses a single slope
- It averages two slopes
- It uses more memory
💡 Hint: Remember the concept of slope averaging.
Question 2
True or False: Modified Euler's Method is more accurate than higher-order methods.
- True
- False
💡 Hint: Think about how different methods compare in accuracy.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Use the Modified Euler’s Method to resolve y(0.4) for dy/dx = y - x^2 with y(0) = 1 over two iterations with a step size of 0.2. Show all calculations.
💡 Hint: Be careful in applying the k1 and k2 calculations stepwise.
Question 2
Demonstrate the Modified Euler’s Method on dy/dx = 2x + 3 with y(0) = 0. Perform four steps with h = 0.25.
💡 Hint: Remember to accurately replace y values after each iteration!
Challenge and get performance evaluation