Practice - Numerical Solutions of ODEs
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Practice Questions
Test your understanding with targeted questions
What is round-off error?
💡 Hint: Think about how numbers are stored in computers.
Define local truncation error.
💡 Hint: Refer to how errors accumulate over steps.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What type of error is caused by the limited precision of computer arithmetic?
💡 Hint: Think about how computers handle digits.
The global truncation error accumulates over how many integration steps?
💡 Hint: Consider what happens to errors when you perform multiple steps.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Assume you have implemented Euler's method for a function. Describe how you would analyze the local truncation error in your implementation.
💡 Hint: Remember to refer to the formula for local truncation error.
Given a numerical method with a known global truncation error of O(h^3), can you reason out the implications for the accuracy of the method if the step size is halved?
💡 Hint: Consider the relationship between step size and the error term.
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