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
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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).
Transcribed Image Text: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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