Using the Euler Method with the step size triangle t=1, estimate x(1) numerically.

adarascarlet80 2022-09-29 Answered
f ( x ) = x and initial condition x ( 0 ) = 1
Using the Euler Method with the step size Δ t = 1, estimate x ( 1 ) numerically.
I so far did:
X n + 1 = X n + f ( x n ) ( 1 )
X 1 = 0
X 2 = 0
I have a similar question on my test tomorrow. Any help will be appreciated
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Answers (2)

Baron Coffey
Answered 2022-09-30 Author has 5 answers
Presumably the differential equation you are working with is x = x with initial condition x ( 0 ) = 1 and the capital X's are the calculated points. You have done the iteration correctly, getting x ( 1 ) = 0. Analytically we can see that the solution is x = e t , so the correct x ( 1 ) = 1 e . You could blacko it with a smaller step size and see that it is more accurate, but that isn't asked for in the question.
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Kwenze0l
Answered 2022-10-01 Author has 2 answers
For you +1 for simply interpreting the question
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