Question
Here's two questions:
1:
2:
Use Euler's method with step size 0.5 to compute the approximate y-values of the solution of the initial-value problem y' = 2 - 5x + 2y, y(0) = 2. Consider the differential equation dy/dx = 4x, with initial condition y(0) = 2. Use Euler's method with two steps to estimate y when x = 1: (Be sure not to round your calculations at each step!) Now use four steps: (Be sure not to round your calculations at each step!) What is the solution to this differential equation (with the given initial condition)? y = What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor = (How close to this is the result you obtained above?)
Explanation / Answer
We have
dy/dx =