Concept explainers
Integrate the following function both analytically and numerically. For the numerical evaluations use
(a) Single application of the trapezoidal rule;
(b) Simpson's 1/3 rule;
(c) Simpson's 3/8 rule;
(d) Multiple application of Simpson's rules, with n = 5;
(e) Boole's rule;
(f) The midpoint method;
(g) The 3-segment–2-point open
(h) The 4-segment–3-point open integration formula.
Compute percent relative errors for the numerical results.
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Chapter 21 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- 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.arrow_forwardT(1)=199.583 T(2)=198.67 T(3)=195.7569 Solve Using Finite Elemental method only need step wise step and correct ansarrow_forwardGiven 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.arrow_forward
- Find 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_forwardFOLLOW THESE STEPS FOR UPVOTE Given Required Diagram Solution Conclusion Do not round off while solving. Question: Consider the figure below. Each tank has a volume of 10 ft³. Conditions on each tank are tabulated as follow: Tank No. 1 2 3 TANK 1 Content Methane Propane Hexane Pressure 70 psia 21 psia 43 psia TANK 1 Temperature 160°F 124°F 110°F TANK 1 k 1.32 1.24 1.39 All separation valves have been opened at the same time. Determine the resulting temperature in °F at equilibrium.arrow_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_forward
- DISCUSSION Before posting to the discussion board, complete the following: The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0arrow_forward6 108 polynomial is used to approximate v8, the answer is: dy 13. of the parametric equations x: 2-3t 3+2t and y =- is dx Use the following information for Questions 14 and 15: 1+t 1+t Using the Newton-Raphson method to determine the critical co-ordinate of the graph y=f(x)=(x)*an (*) (in words x to the power of tan (x)), you will be required to determine f'(x) 14. The expression for f'(x) is: The following tools were required in determining an expression for f'(x): Application of the natural logarithm 15. I. II. The product rule III. Implicit differentiationarrow_forward2. Answer the question completely and write down the given, required and formula that had been used. Provide graph and accurate/comple solution. The value are: V- 1 X- 5 W- 7 Y- 6 Z- 8arrow_forwardx^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.arrow_forwarda) b) c) Use composite Simpson's rule to estimate xe*dx with n=4. Subsequently, find the absolute error. dy dx Given 3y + 2x, where y(0) = 1 and h = 0.2. Approximate the solution for the differential equation for one iteration only by using Runge Kutta method of order two. Set up the Gauss-Siedel iterative equations the following linear system: 6x₁-3x₂ = 2 -x₁ + 3x₂ + x3 =1 x₂ + 4x₂ = 3 (Do not solve)arrow_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
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