Practice Consistency - 18.2.1 | 18. Stability and Convergence of Methods | Mathematics - iii (Differential Calculus) - Vol 4
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

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

18.2.1 - Consistency

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.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the local truncation error?

💡 Hint: Think about what happens in a single step of approximation.

Question 2

Easy

How does the step size ℎ affect consistency?

💡 Hint: Consider what happens as we make steps smaller.

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 does consistency in numerical methods refer to?

  • Local truncation error approaches zero as step size decreases
  • Numerical solutions being exact
  • Stability of numerical methods

💡 Hint: Think about how error behaves as we reduce our step size.

Question 2

True or False: A method can be consistent and not convergent.

  • True
  • False

💡 Hint: Reflect on the relationship between consistency and other properties.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the function y' = -y, apply Euler's method with various step sizes (0.1, 0.01, 0.001) to compute the local truncation error at each step. Analyze how the error decreases.

💡 Hint: Calculate at each step and compare the approximations to the actual solution.

Question 2

Devise a new numerical method and analyze its consistency and stability. Carry out a detailed error analysis comparing it to Euler's method.

💡 Hint: Consider different functions and step sizes in your evaluations.

Challenge and get performance evaluation