Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 12.5, Problem 11E
(a)
To determine
The Eigenvalue and the Eigen functions of the Sturm-Liouville problem as
(b)
To determine
The orthogonality relation for the Eigen functions obtained in sub-part
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9.7 Given the equations
0.5x₁-x2=-9.5
1.02x₁ - 2x2 = -18.8
(a) Solve graphically.
(b) Compute the determinant.
(c) On the basis of (a) and (b), what would you expect regarding
the system's condition?
(d) Solve by the elimination of unknowns.
(e) Solve again, but with a modified slightly to 0.52. Interpret
your results.
12.42 The steady-state distribution of temperature on a heated
plate can be modeled by the Laplace equation,
0=
FT T
+
200°C
25°C
25°C
T22
0°C
T₁
T21
200°C
FIGURE P12.42
75°C
75°C
00°C
If the plate is represented by a series of nodes (Fig. P12.42), cen-
tered finite-divided differences can be substituted for the second
derivatives, which results in a system of linear algebraic equations.
Use the Gauss-Seidel method to solve for the temperatures of the
nodes in Fig. P12.42.
Chapter 12 Solutions
Advanced Engineering Mathematics
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Prob. 9ECh. 12.1 - Prob. 10E
Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 50ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 13ECh. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12 - Prob. 1CRCh. 12 - Prob. 2CRCh. 12 - Prob. 3CRCh. 12 - Prob. 4CRCh. 12 - Prob. 5CRCh. 12 - Prob. 6CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CRCh. 12 - Prob. 13CRCh. 12 - Prob. 14CRCh. 12 - Prob. 16CRCh. 12 - Prob. 17CRCh. 12 - Prob. 19CRCh. 12 - Prob. 20CRCh. 12 - Prob. 21CRCh. 12 - Prob. 22CRCh. 12 - Prob. 23CRCh. 12 - Prob. 24CRCh. 12 - Prob. 25CR
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- 9.22 Develop, debug, and test a program in either a high-level language or a macro language of your choice to solve a system of equations with Gauss-Jordan elimination without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the program using the same system as in Prob. 9.18. Compute the total number of flops in your algorithm to verify Eq. 9.37. FIGURE 9.10 Pseudocode to implement the Gauss-Jordan algorithm with- out partial pivoting. SUB GaussJordan(aug, m, n, x) DOFOR k = 1, m d = aug(k, k) DOFOR j = 1, n aug(k, j) = aug(k, j)/d END DO DOFOR 1 = 1, m IF 1 % K THEN d = aug(i, k) DOFOR j = k, n aug(1, j) END DO aug(1, j) - d*aug(k, j) END IF END DO END DO DOFOR k = 1, m x(k) = aug(k, n) END DO END GaussJordanarrow_forward11.9 Recall from Prob. 10.8, that the following system of equations is designed to determine concentrations (the e's in g/m³) in a series of coupled reactors as a function of amount of mass input to each reactor (the right-hand sides are in g/day): 15c3cc33300 -3c18c26c3 = 1200 -4c₁₂+12c3 = 2400 Solve this problem with the Gauss-Seidel method to & = 5%.arrow_forward9.8 Given the equations 10x+2x2-x3 = 27 -3x-6x2+2x3 = -61.5 x1 + x2 + 5x3 = -21.5 (a) Solve by naive Gauss elimination. Show all steps of the compu- tation. (b) Substitute your results into the original equations to check your answers.arrow_forward
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