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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
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.
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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