(a) Use Euler's method with each of the following step sizes to estimate the value of y(0.4), where y is the solution of the initial-value problem
y' = y, y(0) = 9.
(i) h = 0.4
y(0.4) =
(ii) h = 0.2
y(0.4) =
(iii) h = 0.1
y(0.4) =
(c) The error in Euler's method is the difference between the exact value and the approximate value. Find the errors made in part (a) in using Euler's method to estimate the true value of y(0.4), namely
9e^{0.4}.
(Round your answers to four decimal places.)
h = 0.4 |
error = (exact value) − (approximate value) = |
h = 0.2 |
error = (exact value) − (approximate value) = |
h = 0.1 |
error = (exact value) − (approximate value) = |
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