hw6: `euler_integrate_step` test about computational-thinking HOT 4 OPEN

Can you post a copy of the discussion?

from computational-thinking.

For sure, just added

from computational-thinking.

Thanks for including, but can you explain briefly why it should be reversed?

from computational-thinking.

Sure! It's my understanding that the standard explicit Euler method just uses the information at the beginning of the time step, as stated in the homework assignment:
https://github.com/mitmath/18S191/blob/a5cf7fd3b04d6d285bcd1239d3dcb009342a26fe/homework/homework6/hw6.jl#L210-L212

The test seems to think that we should use the slope at the end of the step: f(a+h) ≃ f(a) + hf'(a + h) instead of the beginning: f(a+h) ≃ f(a) + hf'(a). I don't think this slight modification was mentioned in the homework assignment, which made me think that it probably wasn't the intention to take us down the path of explicit vs implicit numerical methods.

As a sanity check, I just plugged in the test values to both versions, which appear flipped to what it should actually be testing, assuming only the explicit Euler method should be implemented. So, for result = euler_integrate_step(fprime=x -> x^2, fa=10, a=11, h=12) in the test (kwargs added for my own sanity), this corresponds to:

result = f(a) + h*f'(a + h) = 6358

for the correct branch and:

result = f(a) + h*f'(a) = 1462

for the almost branch, when really it should be the other way around.

from computational-thinking.