f ( x ) = − x and initial condition x ( 0 ) = 1Using 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 = 0I have a similar question on my test tomorrow. Any help will be appreciated

Question

f  (  x  )  =  −  x and initial condition   x  (  0  )  =  1Using 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    =  0I have a similar question on my test tomorrow. Any help will be appreciated

Baron Coffey · Accepted Answer

Presumably the differential equation you are working with is       x    ′    =  −  x with initial condition   x  (  0  )  =  1 and the capital   X&#039;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&#039;t asked for in the question.

Kwenze0l · Accepted Answer

For you +1 for simply interpreting the question

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

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