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Consider the logistic differential equation = ry(1 – ) with r, K > 0. This DE has a stable equilibrium at y* = K. What values for h lead to Euler's method converging (locally) to y* = K (Hint: like we did in class for exponential decay using FPI) %3D

Consider the logistic differential equation = ry(1 – ) with r, K > 0. This DE has a stable equilibrium at y* = K. What values for h lead to Euler's method converging (locally) to y* = K (Hint: like we did in class for exponential decay using FPI) %3D

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 16CR
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2. Consider the logistic differential equation = ry(1–) with r, K > 0. This DE has a stable equilibrium at y* = K. What values for h lead to Euler's method converging (locally) to y* = K (Hint: like we did in class for exponential decay using FPI)
Transcribed Image Text:2. Consider the logistic differential equation = ry(1–) with r, K > 0. This DE has a stable equilibrium at y* = K. What values for h lead to Euler's method converging (locally) to y* = K (Hint: like we did in class for exponential decay using FPI)
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