Practice Numerical Solutions of ODEs - 10. | 10. Modified Euler’s Method | Mathematics - iii (Differential Calculus) - Vol 4
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10. - Numerical Solutions of ODEs

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the initial step in the Modified Euler’s Method?

💡 Hint: Think about how slopes represent the rate of change.

Question 2

Easy

True or False: The Modified Euler’s Method is a first-order numerical technique.

💡 Hint: Recall the accuracy level compared to basic Euler’s Method.

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 primary advantage of the Modified Euler’s Method?

  • It is the most accurate method.
  • It requires fewer computations.
  • It improves upon basic Euler’s method.

💡 Hint: Think about why basing on averages instead of single slopes helps.

Question 2

True or False: The Modified Euler's method has only one slope calculation per step.

  • True
  • False

💡 Hint: Recall the steps involved in predicting and correcting.

Solve 2 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Analytically find the solution to the equation dy/dx = 2 - y, with an initial condition y(0)=1 and subsequently use Modified Euler’s Method with h=0.1 to approximate y(0.5). Compare the values and explain the differences.

💡 Hint: Focus on both solving the analytical equation and implementing numerical steps iteratively.

Question 2

Explore the implications of step size on the accuracy of Modified Euler's Method. What would happen if step size h were halved? Perform an analysis between h=0.1 and h=0.05 using the same initial value problem.

💡 Hint: Compare your results closely from both methods while adjusting h.

Challenge and get performance evaluation