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(a) If one solves the ordinary differential equation
using Euler's method find an expression for the local truncation error.
(b) Using the result of (a) above what will the upper bound on the truncation error be for the entire integration range?
(c) Assume that the computation proceeds using a constant integration step h. Show that the upper bound of the global error (i.e. the accumulative error) will be one order of magnitude less than upper bound of the truncation error ( that is, if the global bound of the truncation error is O(hm+1) then the bound for the global error is O(hm)).
(d) How is it possible (sometimes) to make an estimate of these bounds, before carrying out the numerical integration?
Show that when h = h* for the histogram, the contribution to AMISE of the IV and ISB terms is asymptotically in the ratio 2:1. Compare the sensitivity of the AMISE(ch) in Equa
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prove standard deviation of natural natural numbers
(a) Elevation (m) 0 400 800 1200 1600 2000 2400 2800 3200 4000 480
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