13.3 - Runge–Kutta Fourth-Order Method (RK4)
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Practice Questions
Test your understanding with targeted questions
What is the order of accuracy for the RK4 method?
💡 Hint: Think about how many evaluations are made.
What does RK4 stand for?
💡 Hint: Connect the abbreviation to its full name.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What method uses four calculations for slope estimation?
💡 Hint: Consider the number of evaluations each method employs.
True or False: The RK4 method always requires less computational effort than RK2.
💡 Hint: Reflect on the workload involved with each method.
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Challenge Problems
Push your limits with advanced challenges
Given the differential equation dy/dx = sin(x) with y(0) = 0, apply the RK4 method over the interval [0, π/2] with a step size of h = 0.1. Calculate y(π/2).
💡 Hint: Pay close attention to how the sin function behaves within this interval.
Consider the equation dy/dx = (y^2)/x with the initial condition y(1) = 1. Use RK4 to approximate y(2) using h = 0.5.
💡 Hint: Use each k value carefully as y grows rapidly in this region.
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