True/false. Give a brief explanation/counterexample for each part. (i) If f,g: R R are continuous, f(x, z) < g(x, z) for all pairs (r, z) E R, and y = f(x, y) y(0) = Yo Jw' = g(r, w) then for all r E (0, 6), y, w: [0, b] → R solve the IVPS it must be that w(x) > y(x). (ii) Every point of a Cauchy-Euler problem is an ordinary point. (iii) If we use Forward Euler, Backward Euler, and Trapezoidal method to solve a problem Sv = f(x) ly(z0) = Yo BE < Trap << FE. %3D where f is an increasing function, then the iterates obey the relationship

True/false. Give a brief explanation/counterexample for each part. (i) If f,g: R R are continuous, f(x, z) < g(x, z) for all pairs (r, z) E R, and y = f(x, y) y(0) = Yo Jw' = g(r, w) then for all r E (0, 6), y, w: [0, b] → R solve the IVPS it must be that w(x) > y(x). (ii) Every point of a Cauchy-Euler problem is an ordinary point. (iii) If we use Forward Euler, Backward Euler, and Trapezoidal method to solve a problem Sv = f(x) ly(z0) = Yo BE < Trap << FE. %3D where f is an increasing function, then the iterates obey the relationship

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.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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