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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a numerical method.
💡 Hint: Think about how we can calculate using previous values.
Question 2
Easy
What does the step size \( h \) indicate?
💡 Hint: A smaller step size generally leads to more accuracy.
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 a numerical method?
- A way of exact solutions
- An approximation procedure
- Only for linear equations
💡 Hint: Think about how we address complex ODEs.
Question 2
True or False: A smaller step size results in larger local truncation error.
- True
- False
💡 Hint: Recall the relationship between step size and accuracy.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Formulate a numerical method to solve the ODE \( y' = -3y \) with the initial condition \( y(0) = 2 \) using h = 0.5.
💡 Hint: Pay attention to the signs while calculating the next values.
Question 2
Analyze the stability of the numerical method applied to the equation \( y' = -y \). What does your analysis suggest about step size?
💡 Hint: Consider the implications for large values of h.
Challenge and get performance evaluation