Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does stability in numerical methods refer to?
💡 Hint: Think about what happens to a ship in rough waters.
Question 2
Easy
What is the significance of the Lax Equivalence Theorem?
💡 Hint: Remember the relationship between stability and convergence.
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 stability condition for a numerical method?
- |𝑅(ℎ𝜆)| ≤ 1
- |𝑅(ℎ𝜆)| > 1
- |𝑅(ℎ)| = 1
💡 Hint: Remember, if the stability function is greater than 1, errors will grow.
Question 2
True or False: A stable method guarantees convergence.
- True
- False
💡 Hint: Consider the Lax Equivalence Theorem.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the stability condition for a modified Euler method applied to the equation 𝑦' = -𝜆𝑦, where 𝜆 > 0.
💡 Hint: Start by expressing the numerical iteration and finding the corresponding stability function.
Question 2
Apply the Backward Euler method to the equation 𝑦' = -2𝑦 and discuss its properties, leveraging A-stability.
💡 Hint: Evaluate the backward difference and its relation to the stability function.
Challenge and get performance evaluation