EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 27, Problem 17P
Develop a user-friendly program to solve for the largest eigen value with the power method. Test it by duplicating Example 27.7.
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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')
Please answer with The Network Simplex Method
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...
Chapter 27 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 27 - A steady-state heat balance for a rod can be...Ch. 27 - 27.2 Use the shooting method to solve Prob. 27.1....Ch. 27 - 27.3 Use the finite-difference approach with to...Ch. 27 - 27.4 Use the shooting method to solve
Ch. 27 - Solve Prob. 27.4 with the finite-difference...Ch. 27 - 27.7 Differential equations like the one solved...Ch. 27 - 27.8 Repeat Example 27.4 but for three masses....Ch. 27 - 27.9 Repeat Example 27.6, but for five interior...Ch. 27 - Use minors to expand the determinant of...Ch. 27 - 27.11 Use the power method to determine the...
Ch. 27 - 27.12 Use the power method to determine the...Ch. 27 - Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.13 to solve...Ch. 27 - 27.15 Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.15 to solve...Ch. 27 - 27.17 Develop a user-friendly program to solve...Ch. 27 - Develop a user-friendly program to solve for the...Ch. 27 - 27.19 Use the Excel Solver to directly solve...Ch. 27 - Use MATLAB to integrate the following pair of ODEs...Ch. 27 - The following differential equation can be used to...Ch. 27 - 27.22 Use MATLAB or Mathcad to...Ch. 27 - 27.23 Use finite differences to solve the...Ch. 27 - Solve the nondimensionalized ODE using finite...Ch. 27 - 27.25 Derive the set of differential equations for...Ch. 27 - 27.26 Consider the mass-spring system in Fig....Ch. 27 - 27.27 The following nonlinear, parasitic ODE was...Ch. 27 - A heated rod with a uniform heat source can be...Ch. 27 - 27.29 Repeat Prob. 27.28, but for the following...Ch. 27 - 27.30 Suppose that the position of a falling...Ch. 27 - Repeat Example 27.3, but insulate the left end of...
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