EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Textbook Question
Chapter 30, Problem 12P
Develop a user-friendly computer program for the ADI method described in Sec. 30.5. Test it by duplicating Example 30.5.
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Students have asked these similar questions
f(x)=-0.9x? +1.7x+2.5 Calculate the root of the
function given below: a) by Newton-Raphson
method b) by simple fixed-point iteration
method. (f(x)=0) Use x, = 5 as the starting
value for both methods. Use the approximate
relative error criterion of 0.1% to stop
iterations.
3. Using the trial function uh(x) = a sin(x) and weighting function wh(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
25.18 The following is an initial-value, second-order differential equation:
d²x + (5x) dx + (x + 7) sin (wt) = 0
dt²
dt
where
dx (0)
(0) = 1.5 and x(0) = 6
dt
Note that w= 1. Decompose the equation into two first-order differential equations. After the
decomposition, solve the system from t = 0 to 15 and plot the results of x versus time and dx/dt versus time.
Chapter 30 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 30 - 30.1 Repeat Example 30.1, but use the midpoint...Ch. 30 - Repeat Example 30.1, but for the case where the...Ch. 30 - 30.3 (a) Repeat Example 30.1, but for a time step...Ch. 30 - Repeat Example 30.2, but for the case where the...Ch. 30 - Repeat Example 30.3, but for x=1cm.Ch. 30 - 30.6 Repeat Example 30.5, but for the plate...Ch. 30 - 30.7 The advection-diffusion equation is used to...Ch. 30 - 30.8 Develop a user-friendly computer program for...Ch. 30 - 30.9 Modify the program in Prob. 30.8 so that it...Ch. 30 - Develop a user-friendly computer program to...
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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) = 0arrow_forwardFor 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')arrow_forwarda) Name one advantage of the Newton-Raphson method. b) Name one disadvantage of the incremental method.arrow_forward
- 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...arrow_forward2. Let p 19. Then 2 is a primitive root. Use the Pohlig-Hellman method to compute L2(14).arrow_forwardFind the three unknown on this problems using Elimination Method and Cramer's Rule. Attach your solutions and indicate your final answer. Problem 1. 7z 5y 3z 16 %3D 3z 5y + 2z -8 %3D 5z + 3y 7z = 0 Problem 2. 4x-2y+3z 1 *+3y-4z -7 3x+ y+2z 5arrow_forward
- 1:YY IO ZEY H.w.pdf > H.W Use N.R First Method to solve the following function: X3 + 2X -2 Start with X1 = 1arrow_forwardQ-2) Find the solution for the LPP below by using the graphical method? Min Z=4x1+3x2 S.to: x1+2x2<6 2x1+x2<8 x127 x1,x2 ≥ 0 Is there an optimal solution and why if not can you extract it?arrow_forwardThe natural exponential function can be expressed by . Determine e2by calculating the sum of the series for:(a) n = 5, (b) n = 15, (c) n = 25For each part create a vector n in which the first element is 0, the incrementis 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are . Finally, use the MATLAB built-in function sum to add the terms of the series. Compare thevalues obtained in parts (a), (b), and (c) with the value of e2calculated byMATLAB.arrow_forward
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