EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 8.1, Problem 4E
Interpretation Introduction
Interpretation:
To find the Eigenvalues at the stable fixed point in terms of μ and to show that one Eigenvalue tends to 0 as μ→0
Concept Introduction:
Fixed point of a differential equation is a point where f(x*) = 0 ; while substitution f(x*) = ˙x is used and x&*#x00A0;is a fixed point.
Values of a parameters which differential equation have a non-zero solution under given conditions are called Eigenvalues.
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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.
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 GaussJordan
Chapter 8 Solutions
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Prob. 4ECh. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Prob. 17ECh. 8.3 - Prob. 1ECh. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.5 - Prob. 1ECh. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12E
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