Practice Improved Euler’s Method (Heun’s Method) - 7.2.3 | 7. Numerical Solution of Ordinary Differential Equations (ODEs) | Mathematics - iii (Differential Calculus) - Vol 4
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Improved Euler’s Method (Heun’s Method)

7.2.3 - Improved Euler’s Method (Heun’s Method)

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Practice Questions

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Question 1 Easy

What is the main advantage of Heun's Method over Euler's Method?

💡 Hint: Consider the aspect of slope calculations.

Question 2 Easy

What does ODE stand for?

💡 Hint: Think about the types of equations involving derivatives.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the main purpose of Heun's Method?

To provide an accurate solution to linear equations
To improve the accuracy of Euler's Method
To simplify ordinary differential equations

💡 Hint: Think about why we need numerical methods.

Question 2

True or False: Heun’s Method requires twice the function evaluations compared to Euler's Method.

True
False

💡 Hint: Consider how many times we calculate the function in each method.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Using Heun's Method, calculate an approximation of the solution for the ODE dy/dx = y - x^2 + 1 with initial value y(0) = 0.5 at x = 0.2; use a step size of 0.1.

💡 Hint: Break the problem down into steps: evaluate the function, predict, and then correct.

Challenge 2 Hard

A population is modeled by the equation dP/dt = rP where P(0) = 1000, r=0.03. Predict the population at t=1 using Heun's Method with h=0.1.

💡 Hint: Apply the Heun's method formula and keep track of your computations carefully.

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