Practice Improved Euler’s Method (heun’s Method) (7.2.3) - Numerical Solution of Ordinary Differential Equations (ODEs)

Practice: Improved Euler’s Method (Heun’s Method)

Lesson 7.2.3Numerical Solution of Ordinary Differential Equations (ODEs)

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9 questions

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6 sample questions

Question 1.
What is the main advantage of Heun's Method over Euler's Method?
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Consider the aspect of slope calculations.
Question 2.
What does ODE stand for?
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Think about the types of equations involving derivatives.
3Question 3.
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
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Think about why we need numerical methods.
4Question 4.
True or False: Heun’s Method requires twice the function evaluations compared to Euler's Method.
- True
- False
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Consider how many times we calculate the function in each method.
Question 5.
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.
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Break the problem down into steps: evaluate the function, predict, and then correct.
Question 6.
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.
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Apply the Heun's method formula and keep track of your computations carefully.

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