Fluid Mechanics: Fundamentals and Applications
Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 15, Problem 25P
To determine

To sketch:

Computational domain of the given image and boundary condition.

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The exercise concerns the Gauss-Legendre integration method for integrals of the form that is in the picture i uploaded with the difference that the integration will not be done at the N+1 specific points (or Gauss nodes: x_0, x_1, …, x_N) as tabulated in your book, but at N+1 points placed arbitrarily (but in monotonically increasing order) in the interval [-1, 1]. If f(x) is a polynomial of degree K, what is the largest value of K (expressed, obviously, as a function of N) for which the integral I is calculated exactly. Provide a convincing numerical demonstration of your answer for N=3 (choosing your own values for x_0, x_1, x_2, x_3).
Please show how to derive cagliotti function.
Kindly solve with full solution and explain. Thank you very much
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