18.1.2 - Numerical Method
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Practice Questions
Test your understanding with targeted questions
Define a numerical method.
💡 Hint: Think about how we can calculate using previous values.
What does the step size \( h \) indicate?
💡 Hint: A smaller step size generally leads to more accuracy.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a numerical method?
💡 Hint: Think about how we address complex ODEs.
True or False: A smaller step size results in larger local truncation error.
💡 Hint: Recall the relationship between step size and accuracy.
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Challenge Problems
Push your limits with advanced challenges
Formulate a numerical method to solve the ODE \( y' = -3y \) with the initial condition \( y(0) = 2 \) using h = 0.5.
💡 Hint: Pay attention to the signs while calculating the next values.
Analyze the stability of the numerical method applied to the equation \( y' = -y \). What does your analysis suggest about step size?
💡 Hint: Consider the implications for large values of h.
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