Numerical Methods For Engineers, 7 Ed
Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 27, Problem 3P

Use the finite-difference approach with Δ x = 1 to solve Prob. 27.1.

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1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to this behavior?
1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).
Define sinc(x) = sin(x)/x, except with the singularity removed.  Differentiate sinc(x) once and twice.

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Numerical Methods For Engineers, 7 Ed

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