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For the function g(x) = x = (1 + c)x + cx, show that a = 1 is a fixed point and hich values of the constant c the iteration sequence for initial conditions sufficiently erge. For what values of c, if any, is the convergence quadratic? Verify your results numerically.

For the function g(x) = x = (1 + c)x + cx, show that a = 1 is a fixed point and hich values of the constant c the iteration sequence for initial conditions sufficiently erge. For what values of c, if any, is the convergence quadratic? Verify your results numerically.

Advanced Engineering Mathematics
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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= (10 points) For the function g(x) = x = (1 + c) x + cx³, show that a 1 is a fixed point and determine for which values of the constant c the iteration sequence for initial conditions sufficiently close to a converge. For what values of c, if any, is the convergence quadratic? Verify your results graphically and numerically.
Transcribed Image Text:= (10 points) For the function g(x) = x = (1 + c) x + cx³, show that a 1 is a fixed point and determine for which values of the constant c the iteration sequence for initial conditions sufficiently close to a converge. For what values of c, if any, is the convergence quadratic? Verify your results graphically and numerically.
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