7. Consider solving the initial value problem dy -= yt? – 1.1y, v(t = 0) = 1, %3D dt from t = 0 to t 1. (a) Find the true solution analytically using separation of variables. Calculate the true values of y(t) for a step size h = 0.5. Use the result to calculate the true relative error in percentage for each of the numerical solutions below. (b) Solve numerically using Euler's method using step size h = 0.5. (c) Solve numerically using fourth order Runge-Kutta method with step size h = 0.5.

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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7. Consider solving the initial value problem
dy
y' =
= yt? - 1.1y, y(t = 0) = 1,
dt
%3D
from t = 0 to t = 1.
(a) Find the true solution analytically using separation of variables. Calculate the true
values of y(t) for a step size h = 0.5. Use the result to calculate the true relative error
in percentage for each of the numerical solutions below.
(b) Solve numerically using Euler's method using step size h = 0.5.
(c) Solve numerically using fourth order Runge-Kutta method with step size h 0.5.
8. Consider solving the second order ODE
dy
+ 0.6 + 8y 0
dz?
dy
dz
with initial conditions y(0) = 4 and y'(0) = 0. Solve numerically using fourth order Runge-
Kutta method with step size h = 0.5 from a =
to a 1.
Transcribed Image Text:7. Consider solving the initial value problem dy y' = = yt? - 1.1y, y(t = 0) = 1, dt %3D from t = 0 to t = 1. (a) Find the true solution analytically using separation of variables. Calculate the true values of y(t) for a step size h = 0.5. Use the result to calculate the true relative error in percentage for each of the numerical solutions below. (b) Solve numerically using Euler's method using step size h = 0.5. (c) Solve numerically using fourth order Runge-Kutta method with step size h 0.5. 8. Consider solving the second order ODE dy + 0.6 + 8y 0 dz? dy dz with initial conditions y(0) = 4 and y'(0) = 0. Solve numerically using fourth order Runge- Kutta method with step size h = 0.5 from a = to a 1.
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