10.1.5 - Derivation (Brief Insight)
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Practice Questions
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What is the main advantage of the Modified Euler's Method?
💡 Hint: What does it use to enhance accuracy?
What does k1 represent in Modified Euler's Method?
💡 Hint: Think about the estimation of the slope from initial conditions.
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which method improves upon basic Euler's Method?
💡 Hint: What do you know about the function evaluations?
True or False: The Modified Euler’s Method requires two function evaluations per step.
💡 Hint: Think about the steps in the algorithm.
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Challenge Problems
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Solve the initial value problem dy/dx = 2x + y, with y(1)=3 using the Modified Euler's Method with h=0.05 to find y(1.1).
💡 Hint: Remember to calculate both slopes in each step.
Compare the results of Modified Euler's and basic Euler's Method for dy/dx = x^2 + y, y(0)=2 at x=0.2 with h=0.1. What are the differences in the results?
💡 Hint: Look at the averages and steepness of the slopes being calculated.
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