EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 7, Problem 24P
Develop an M-file function for the modified secant method based on Fig. 6.4 and Sec. 6.3.2. Along with the initial guess and the perturbation fraction, pass the function as an argument. Test it by duplicating the computation from Example 6.8.
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Consider the function p(x) = x² - 4x³+3x²+x-1. Use Newton-Raphson's method with initial guess of 3. What's the updated value of the root at the end of the second
iteration?
Type your answer...
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
For the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3:
Q1) Using Matlab to employ the Euler Method (Sect 2.4)
Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5
close all
clear all
% Let's program exact soln
for i=1:5
x_exact(i)=0.5*i-0.5;
y_exact(i)=-x_exact(i)-1+exp(x_exact(i));
end
plot(x_exact,y_exact,'b')
% now for Euler's
h=0.5
x_EM(1)=0;
y_EM(1)=0;
for i=2:5
x_EM(i)=x_EM(i-1)+h;
y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1)));
end
hold on
plot (x_EM,y_EM,'r')
% Improved Euler's Method
h=0.5
x_IE(1)=0;
y_IE(1)=0;
for i=2:1:5
kA=x_IE(i-1)+y_IE(i-1);
u=y_IE(i-1)+h*kA;
x_IE(i)=x_IE(i-1)+h;
kB=x_IE(i)+u;
k=(kA+kB)/2;
y_IE(i)=y_IE(i-1)+h*k;
end
hold on
plot(x_IE,y_IE,'k')
Chapter 7 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 7 - Divide a polynomial f(x)x47.5x3+14.5x2+3x20 by the...Ch. 7 - Divide a polynomial f(x)=x55x4+x36x27x+10 by the...Ch. 7 - Prob. 3PCh. 7 - 7.4 Use Müller’s method or MATLAB to determine the...Ch. 7 - 7.6 Develop a program to implement Muller’s...Ch. 7 - 7.7 Use the program developed in Prob. 7.6 to...Ch. 7 - Develop a program to implement Bairstows method....Ch. 7 - Use the program developed in Prob. 7.8 to...Ch. 7 - Determine the real root of x3.5=80 with Excel,...Ch. 7 - 7.11 The velocity of a falling parachutist is...
Ch. 7 - Determine the roots of the simultaneous nonlinear...Ch. 7 - 7.13 Determine the roots of the simultaneous...Ch. 7 - 7.14 Perform the identical MATLAB operations as...Ch. 7 - 7.15 Use MATLAB or Mathcad to determine the...Ch. 7 - A two-dimensional circular cylinder is placed in a...Ch. 7 - 7.17 When trying to find the acidity of a...Ch. 7 - Consider the following system with three unknowns...Ch. 7 - 7.19 In control systems analysis, transfer...Ch. 7 - Develop an M-file function for bisection in a...Ch. 7 - 7.21 Develop an M-fi le function for the...Ch. 7 - 7.22 Develop an M-fi le function for the...Ch. 7 - Develop an M-fi le function for the secant method...Ch. 7 - Develop an M-file function for the modified secant...
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