4 - Numerical Solutions of Ordinary Differential Equations
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Practice Questions
Test your understanding with targeted questions
Define an ordinary differential equation (ODE).
💡 Hint: Think about how these equations relate to functions.
What does Euler's method calculate at each step?
💡 Hint: Refer to the Euler's Method formula.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Euler's method use to update the solution?
💡 Hint: Think about how derivatives relate to rates of change.
True or False: The Runge-Kutta method is less accurate than Euler's method.
💡 Hint: Have you compared both methods in terms of step calculations?
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Challenge Problems
Push your limits with advanced challenges
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?
💡 Hint: Consider how each step builds on the last.
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.
💡 Hint: Focus on calculating the k values carefully.
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