4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by 1+t 1+y the Butcher array below to estimate solutions to the IVP y' = with y(1) = 2 and t = [1,2]. Start by using both methods to estimate y(2) with h = .5 and computing the error. Then select several values of h ≤ 10–5 to provide estimations of y(1.001) and y(2) for each method. What choice of h that you computed optimizes the error for each method? How do the methods compare for each t value? 0 1/3 1/3 2/3 -1/3 1 1 1 -1 1 1/8 3/8 3/8 1/8
4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by 1+t 1+y the Butcher array below to estimate solutions to the IVP y' = with y(1) = 2 and t = [1,2]. Start by using both methods to estimate y(2) with h = .5 and computing the error. Then select several values of h ≤ 10–5 to provide estimations of y(1.001) and y(2) for each method. What choice of h that you computed optimizes the error for each method? How do the methods compare for each t value? 0 1/3 1/3 2/3 -1/3 1 1 1 -1 1 1/8 3/8 3/8 1/8
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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Please please solve
![4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by
=
1+t
1+y
with y(1) = 2 and t = [1,2].
the Butcher array below to estimate solutions to the IVP y' =
Start by using both methods to estimate y(2) with h = .5 and computing the error. Then select
several values of h≤ 10-5 to provide estimations of y(1.001) and y(2) for each method. What
choice of h that you computed optimizes the error for each method? How do the methods compare
for each t value?
0
1/3 1/3
2/3 -1/3 1
1
1
-1 1
1/8 3/8 3/8 1/8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F444a28ed-437f-4929-a1ec-5907998afa93%2Fcd341249-d4b4-4d02-bc7f-58cfbccc4083%2Fk6it8yj_processed.png&w=3840&q=75)
Transcribed Image Text:4. This problems asks you to use both the Forward Euler and the Runge-Kutta method specified by
=
1+t
1+y
with y(1) = 2 and t = [1,2].
the Butcher array below to estimate solutions to the IVP y' =
Start by using both methods to estimate y(2) with h = .5 and computing the error. Then select
several values of h≤ 10-5 to provide estimations of y(1.001) and y(2) for each method. What
choice of h that you computed optimizes the error for each method? How do the methods compare
for each t value?
0
1/3 1/3
2/3 -1/3 1
1
1
-1 1
1/8 3/8 3/8 1/8
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