The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in (m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in (m) from t = 0 to 10 (s). Determine the true value of the displacement and the true percent relative error of the numerical result, lel.
The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in (m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in (m) from t = 0 to 10 (s). Determine the true value of the displacement and the true percent relative error of the numerical result, lel.
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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![The following equation defines how the velocity of a slow-moving vehicle varies with time where the
velocity V is in [m/s] and time t is in [s].
V = 0.5t + 2t/2
a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10
[s). Continue iterating until the approximate percent relative error leal is less than 1%.
b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in [m]
from t = 0 to 10 (s]. Determine the true value of the displacement and the true percent relative
error of the numerical result, lel.
c) Use Richardson Extrapolation to determine the acceleration of the vehicle at t = 5 [s). Use step
sizes of h, = 1 (s) and h, = 0.5 (s) and use the forward difference approximation of O(h) for the
initial approximations. Determine the true value of the acceleration and the true percent relative
error, leel, of the numerical approximation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7659519e-735b-4a87-8833-f1afaf109176%2F220661d6-ab8a-41b5-a460-b0dcda765864%2Fcy7hul_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following equation defines how the velocity of a slow-moving vehicle varies with time where the
velocity V is in [m/s] and time t is in [s].
V = 0.5t + 2t/2
a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10
[s). Continue iterating until the approximate percent relative error leal is less than 1%.
b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in [m]
from t = 0 to 10 (s]. Determine the true value of the displacement and the true percent relative
error of the numerical result, lel.
c) Use Richardson Extrapolation to determine the acceleration of the vehicle at t = 5 [s). Use step
sizes of h, = 1 (s) and h, = 0.5 (s) and use the forward difference approximation of O(h) for the
initial approximations. Determine the true value of the acceleration and the true percent relative
error, leel, of the numerical approximation.
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