EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 2, Problem 5P
Develop, debug, and document a program for Prob. 2.4 in either a high-level language or a macro language of your choice. Employ the library function for the sine in your computer to determine the true value. Have the program print out the series approximation and the error at each step. As a test case, employ the program to compute
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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
Consider the following Initial Value Problem (IVP) dy /at = -t * sin (y); y(t = 0) =1
Solve for y(t=0.5) using
a) Forward Euler method with At = 0.25. (Solve by hand)
Develop a Matlab script that solves for y (t = 5) using Forward Euler method. Use
the time step levels given below and plot t vs y in the same plot. Include the plot
with the right format (axis labels, legends, ...) in your solution sheet and include
your Matlab script in the solution as well.
i) At = 0.25
ii) At = 0.125
b) Backward Euler method with At = 0.25 (Solve by hand)
As4.
This is my third time asking this question. Please DO NOT copy and paste someone else's work or some random notes. I need an answer to this question.
There is a mass attached to a spring which is fixed against a wall. The spring is compressed and then released. Friction and is neglected. The velocity and displacement of the mass need to be modeled with an equation or set of equations so that various masses and spring constants can be input into Matlab and their motion can be observed. Motion after being released is only important, the spring being compressed is not important. This could be solved with dynamics, Matlab, there are multiple approaches.
Chapter 2 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 2 - 2.1 Write pseudocode to implement the flowchart...Ch. 2 - Prob. 2PCh. 2 - 2.3 Develop, debug, and document a program to...Ch. 2 - The sine function can be evaluated by the...Ch. 2 - 2.5 Develop, debug, and document a program for...Ch. 2 - The following algorithm is designed to determine a...Ch. 2 - The divide and average method, an old-time method...Ch. 2 - 2.8 An amount of money P is invested in an account...Ch. 2 - 2.9 Economic formulas are available to compute...Ch. 2 - 2.10 The average daily temperature for an area can...
Ch. 2 - Develop, debug, and test a program in either a...Ch. 2 - 2.12 The bubble sort is an inefficient, but...Ch. 2 - Figure P2.13 shows a cylindrical tank with a...Ch. 2 - 2.14 Two distances are required to specify the...Ch. 2 - Develop a well-structured function procedure that...Ch. 2 - Prob. 16PCh. 2 - Develop well-structured programs to (a) determine...Ch. 2 - 2.18 Piecewise functions are sometimes useful when...Ch. 2 - Develop a well-structured function to determine...Ch. 2 - 2.20 Develop a well-structured function to...Ch. 2 - 2.21 Manning’s equation can be used to compute the...Ch. 2 - 2.22 A simply supported beam is loaded as shown in...Ch. 2 - ThevolumeV of liquid in ahollow horizontal...Ch. 2 - 2.24 Develop a well-structured program to compute...Ch. 2 - The pseudocode in Fig. P2.25 computes the...Ch. 2 - 2.26 The height of a small rocket y can be...Ch. 2 - 2.27 As depicted in Fig. P2.27, a water tank...
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