Solve the following ODE: y' t² y cos(y+t) ³, (a) using the following schemes: i. Leapfrog. y (0) = 1, t = [0,3],
Solve the following ODE: y' t² y cos(y+t) ³, (a) using the following schemes: i. Leapfrog. y (0) = 1, t = [0,3],
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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![3. Solve the following ODE:
y' = t² y cos(y+t)³, y(0) = 1,
using the following schemes:
i. Leapfrog.
ii. Trapezoidal.
iii. Second order Runge-Kutta.
iv. Fourth order Runge-Kutta.
t = [0,3],
(b) Investigate experimentally the order of accuracy of each scheme by performing a
convergence study. Plot the norm of the relative error L vs. the grid size h on
a log-log scale and estimate the order of accuracy. (At least show five solutions.)
(c) Discuss your results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed051053-4bf3-451a-ac87-e1db40d07cdc%2F369ad0c4-22a8-45f3-bf6e-417ae9faf96a%2Fcc4isu_processed.png&w=3840&q=75)
Transcribed Image Text:3. Solve the following ODE:
y' = t² y cos(y+t)³, y(0) = 1,
using the following schemes:
i. Leapfrog.
ii. Trapezoidal.
iii. Second order Runge-Kutta.
iv. Fourth order Runge-Kutta.
t = [0,3],
(b) Investigate experimentally the order of accuracy of each scheme by performing a
convergence study. Plot the norm of the relative error L vs. the grid size h on
a log-log scale and estimate the order of accuracy. (At least show five solutions.)
(c) Discuss your results.
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