Practice Numerical Solutions Of Ordinary Differential Equations (4) - Numerical Solutions of Ordinary Differential Equations

Practice: Numerical Solutions of Ordinary Differential Equations

Lesson 4Numerical Solutions of Ordinary Differential Equations

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define an ordinary differential equation (ODE).
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Think about how these equations relate to functions.
Question 2.
What does Euler's method calculate at each step?
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Refer to the Euler's Method formula.
3Question 3.
What does Euler's method use to update the solution?
- The last two function values
- The last function value and its derivative
- Only the last function value
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Think about how derivatives relate to rates of change.
4Question 4.
True or False: The Runge-Kutta method is less accurate than Euler's method.
- True
- False
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Have you compared both methods in terms of step calculations?
Question 5.
Using Euler's Method, solve the differential equation dydt=3y for y(0)=1 with a step size of h=0.2 for 5 iterations. How does this compare to the actual solution?
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Consider how each step builds on the last.
Question 6.
Implement the fourth-order Runge-Kutta method for the same function dydt=3y, y(0)=1, over the same 5 iterations. Compare the RK4 output to the values you obtained from Euler's method.
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Focus on calculating the k values carefully.

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