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Esci 118 - Numerical Methods To Engineering Problems: Name: Offering No.: Student Id: Mobile No

1) The document provides instructions for a numerical methods quiz with 3 parts. Students are assigned 1 of 3 problems in Part I based on their student ID. They must solve the problem using Gauss elimination, Gauss-Jordan, or LU decomposition methods. 2) Part II involves solving a system of 13 equations to calculate axial forces in a 13-member pin-connected truss using Gauss-Seidel iteration, and determining if the solution converges from an initial guess of zero. 3) Part III requires finding the solution to two simultaneous equations using iterative methods, starting at the point (1.5, 3.5) and iterating until the tolerance of 10^-5 is reached.

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92 views2 pages

Esci 118 - Numerical Methods To Engineering Problems: Name: Offering No.: Student Id: Mobile No

1) The document provides instructions for a numerical methods quiz with 3 parts. Students are assigned 1 of 3 problems in Part I based on their student ID. They must solve the problem using Gauss elimination, Gauss-Jordan, or LU decomposition methods. 2) Part II involves solving a system of 13 equations to calculate axial forces in a 13-member pin-connected truss using Gauss-Seidel iteration, and determining if the solution converges from an initial guess of zero. 3) Part III requires finding the solution to two simultaneous equations using iterative methods, starting at the point (1.5, 3.5) and iterating until the tolerance of 10^-5 is reached.

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jejomar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Name: Offering No.

:
Student ID: Mobile No:

ESCi 118 – Numerical Methods to Engineering Problems


QUIZ NO. 3

Due Date: Nov. 26, 2020

Instructions:
 Write a report that contains description of the problems, plan of solution, and
interpretation of results. Explain clearly how each solution was obtained and show
sample test runs whenever applicable.
 Submit a softcopy of this quiz by uploading it to our virtual classroom under Quiz
No.3 (only when you cannot submit it through the virtual classroom that you need to
email it to grace.curay@vsu.edu.ph).

PART I

Quiz No. 3 contains Part I, Part II, and III. In Part I, you are supposed to answer one (1)
problem only. Problem 1, Problem 2, and Problem 3 will be solved by a student with a last
digit number (0-3), (4-6), and (7-9) respectively of his/her Student ID.

Solve your assigned problem by using the three direct methods discussed in class namely:
Gauss Elimination, Gauss-Jordan, and LU Decomposition by Crout’s.

Problem 1:
2 x1  x2  x3  2 x4  0
x1  2 x2  x3  4 x4  3
3 x1  x2  2 x3  x4  3
 x1  2 x2  x3  2 x4  13

Problem 2:
2 x1  x2  x3  4 x4  19
 x1  2 x2  x3  2 x4  3
2 x1  4 x2  2 x3  x4  25
 x1  x2  x3  2 x4  5
Problem 3:

4 x1  3 x2  2 x3  x4  17
2 x1  x2  2 x3  4 x4  11
x1  2 x2  2 x3  x4  8
 2 x1  4 x2  5 x3  x4  15
PART II

The axial force Fi in each of the 13-member pin-connected truss, shown in the figure below,
can be calculated by solving the following system of 13 equations:

F2  0.707 F1  0, F3  0.707 F1  2000  0


0.707 F1  F4  6229  0, - F2  0.659 F5  F6  0
 F4  0.753F5  600  0, - F3  0.659 F5  F7  0
0.753F5  F8  0, - F6  0.659 F9  F10  0
 F8  0.753F9  800  0, - F7  0.659 F9  F11  0
0.753F9  F12  2429  0, - F10  0.707 F13  0
 F12  0.707 F13  600  0

Solve the system of equations using Gauss-Seidel iteration. Does the solution converge for a
starting (guess) vector whose elements are all zero?

PART III (15 points)

Find the solution of the equations:

f ( x, y )  x 2  xy  10  0
g ( x, y )  y  3xy 2  57  0

By taking the starting point as (1.5, 3.5) and TOL= 1x10 5 .

Prepared by:

Engr. Ma. Grace C. Sumaria

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