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2 cards from this section. Quick, good the night before a test.
What does an Initial Value Problem (IVP) specify?
Think about initial conditions.
Name one numerical method used to solve ODEs.
It's the simplest one.
What is the main goal when using numerical methods for ODEs?
Think about what happens if you can't solve it exactly.
True or False: Euler's Method is the most accurate method for solving ODEs.
Consider how accuracy changes with different methods.
Using Euler's Method, estimate the solution for the ODE dy/dx = y - x^2 + 1 with initial condition y(0) = 0.5 using a step size of 0.2. What is y(0.2) and y(0.4)?
Use the formula y(n+1) = y(n) + h*f(x(n), y(n)).
For the ODE dy/dx = 2y/x and initial condition y(1) = 1, apply the Runge-Kutta method with h = 0.1 to find y(1.1) and y(1.2). Show your calculations.
The RK4 method has four slopes to calculate for each step.
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