which one the fixed points is stable and unstable from the fig First, we will use equation (7.129) to calculate approximations to the re-ciprocals of x. This case corresponds to m = -1. Hence, equation (7.129)becomesYk+1 =Yk (2 – xyk).(7.130)The geometric methods of Section 2.7 may be used to investigate the proper-ties of this nonlinear difference equation.In Figure 7.2, equation (7.130) is plotted. These results follow from acareful examination of this graph:Yk+1(0, 0)YkFIGURE 7.2: Computing reciprocals; Yk+1 =Yk (2 – xyk).

Concept Used : A fixed point a is stable if derivative of f(x) at a is strictly less than 0, and…

Answered: Yk+1 (0, 0) Ук

Math

Advanced Math

Yk+1 (0, 0) Ук

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

which one the fixed points is stable and unstable from the fig

First, we will use equation (7.129) to calculate approximations to the re-
ciprocals of x. This case corresponds to m = -1. Hence, equation (7.129)
becomes
Yk+1 =
Yk (2 – xyk).
(7.130)
The geometric methods of Section 2.7 may be used to investigate the proper-
ties of this nonlinear difference equation.
In Figure 7.2, equation (7.130) is plotted. These results follow from a
careful examination of this graph:
Yk+1
(0, 0)
Yk
FIGURE 7.2: Computing reciprocals; Yk+1 =
Yk (2 – xyk).

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