EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 18, Problem 17P
Develop, debug, and test a program in either a high-level language or macro language of your choice to implement Newton's interpolating polynomial based on Fig. 18.7.
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3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find
an approximate solution to the following boundary value problems by determining the value
of coefficient a. For each one, also find the exact solution using Matlab and plot the exact
and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution,
and (iii) plotting the solution)
a.
(U₁xx -2 = 0
u(0) = 0
u(1) = 0
b. Modify the trial function and find an approximation for the following boundary value
problem. (Hint: you will need to add an extra term to the function to make it satisfy
the boundary conditions.)
(U₁xx-2 = 0
u(0) = 1
u(1) = 0
Given the data below:
Xo = 1
X1= 2
x2 = 4
Axo) = 2
Ax1) = 3
Ax2 :
= 8
(i) Calculate the second-order interpolating polynomial using the method of the Newton's interpolating
polynomial.
(ii) Use the interpolating polynomial in (i) to calculate the approximated/interpolated functional value at x = 3,
i.e., (3).
(iii)Calculate the percentage relative error if the true value of f(3) is 4.8.
Help me solve this USING MATLAB
Chapter 18 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 18 - 18.1 Estimate the common logarithm of 10 using...Ch. 18 - 18.2 Fit a second-order Newton’s interpolating...Ch. 18 - 18.3 Fit a third-order Newton’s interpolating...Ch. 18 - Repeat Probs. 18.1 through 18.3 using the Lagrange...Ch. 18 - 18.5 Given these...Ch. 18 - 18.6 Given these data
x 1 2 3 5 7 8
...Ch. 18 - Repeat Prob. 18.6 using Lagrange polynomials of...Ch. 18 - 18.8 The following data come from a table that was...Ch. 18 - 18.9 Use Newton’s interpolating polynomial to...Ch. 18 - Use Newtons interpolating polynomial to determine...
Ch. 18 - 18.11 Employ inverse interpolation using a cubic...Ch. 18 - 18.12 Employ inverse interpolation to determine...Ch. 18 - 18.13 Develop quadratic splines for the first five...Ch. 18 - 18.14 Develop cubic splines for the data in Prob....Ch. 18 - Determine the coefficients of the parabola that...Ch. 18 - Determine the coefficients of the cubic equation...Ch. 18 - 18.17 Develop, debug, and test a program in either...Ch. 18 - 18.18 Test the program you developed in Prob....Ch. 18 - 18.19 Use the program you developed in Prob. 18.17...Ch. 18 - Use the program you developed in Prob. 18.17 to...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - 18.22 A useful application of Lagrange...Ch. 18 - Develop, debug, and test a program in either a...Ch. 18 - Use the software developed in Prob. 18.23 to fit...Ch. 18 - Use the portion of the given steam table for...Ch. 18 - The following is the built-in humps function that...Ch. 18 - 18.28 The following data define the sea-level...Ch. 18 - 18.29 Generate eight equally-spaced points from...Ch. 18 - 18.30 Temperatures are measured at various points...
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