Repeat Exercise 1 using the Runge-Kutta fourth-order method. In Exercise 1 a. y' = 9y, 0 t

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Repeat Exercise 1 using the Runge-Kutta fourth-order method.

In Exercise 1

a. y' = −9y, 0≤ t ≤ 1, y(0) = e, with h = 0.1; actual solution y(t) = e1−9t .

b. y' = −20(y−t2)+2t, 0≤ t ≤ 1, y(0) = 1/3 , with h = 0.1; actual solution y(t) = t2+1/3 e−20t .

c. y' = −20y + 20 sin t + cos t, 0 ≤ t ≤ 2, y(0) = 1, with h = 0.25; actual solution y(t) = sin t + e−20t

d. y' = 50/y−50y, 0≤ t ≤ 1, y(0) = √2, with h = 0.1; actual solution y(t) = (1+e−100t)1/2.

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Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

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