The following ODE governs the vertically the ODE given above and find a function for the vertical position of the ball y(t) and calculate the initial velocity of the ball at t = 0. y(t = 0.5) => y1 (t = 1.0) => y2 y(t = 1.5) => y3 (t = 2.0) => y4 ylt = 2.5) => y5 finite difference equation day dtª b) Discretize the ODE by hand using the finite difference method and end up with a linear system Ay = b where A is of size 5x5. (This means you should have 5 equations and 5 unknown y-positions of the ball. -> Position for the time levels [0.5, 1.0, 1.5, 2.0, 2.5]) de a =-9 le= ≈ -2y+y₁+1+1 (At)ª c) Row reduce the augmented matrix [A[b] in b) and convert it into Echolon form (upper triangular form in this case too.) and solve using Backward substitution d) Write a Matlab script that can generate the A matrix and the b vector and solves for the position of the ball at the time intervals [0.25, 0.50, 0.75, 1.00,..., 2.75] and plot t vs y
The following ODE governs the vertically the ODE given above and find a function for the vertical position of the ball y(t) and calculate the initial velocity of the ball at t = 0. y(t = 0.5) => y1 (t = 1.0) => y2 y(t = 1.5) => y3 (t = 2.0) => y4 ylt = 2.5) => y5 finite difference equation day dtª b) Discretize the ODE by hand using the finite difference method and end up with a linear system Ay = b where A is of size 5x5. (This means you should have 5 equations and 5 unknown y-positions of the ball. -> Position for the time levels [0.5, 1.0, 1.5, 2.0, 2.5]) de a =-9 le= ≈ -2y+y₁+1+1 (At)ª c) Row reduce the augmented matrix [A[b] in b) and convert it into Echolon form (upper triangular form in this case too.) and solve using Backward substitution d) Write a Matlab script that can generate the A matrix and the b vector and solves for the position of the ball at the time intervals [0.25, 0.50, 0.75, 1.00,..., 2.75] and plot t vs y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The following ODE governs the vertically the ODE given above and find a function for the vertical
position of the ball y(t) and calculate the initial velocity of the ball at t = 0.
day
dtª
de 2
b) Discretize the ODE by hand using the finite difference method and end up with a linear system Ay = b
where A is of size 5x5. (This means you should have 5 equations and 5 unknown y-positions of the ball.
-> Position for the time levels [0.5, 1.0, 1.5, 2.0, 2.5])
y(t = 0.5) => y1
y(t = 1.0) => y2
y(t = 1.5) => y3
ylt = 2.0) => y4
y(t = 2.5) => y5
finite difference equation
=-9
le=e₁
-2yi+yi+yi+s
(At)a
c) Row reduce the augmented matrix [A[b] in b) and convert it into Echolon form (upper triangular form
in this case too.) and solve using Backward substitution
d) Write a Matlab script that can generate the A matrix and the b vector and solves for the position of
the ball at the time intervals [0.25, 0.50, 0.75, 1.00,..., 2.75] and plot t vs y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc950c62e-cc0c-403f-861c-8d3b3e11c452%2Fb46a7bb2-5acd-46d6-8a32-8e5710909a90%2F7c5vdnv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following ODE governs the vertically the ODE given above and find a function for the vertical
position of the ball y(t) and calculate the initial velocity of the ball at t = 0.
day
dtª
de 2
b) Discretize the ODE by hand using the finite difference method and end up with a linear system Ay = b
where A is of size 5x5. (This means you should have 5 equations and 5 unknown y-positions of the ball.
-> Position for the time levels [0.5, 1.0, 1.5, 2.0, 2.5])
y(t = 0.5) => y1
y(t = 1.0) => y2
y(t = 1.5) => y3
ylt = 2.0) => y4
y(t = 2.5) => y5
finite difference equation
=-9
le=e₁
-2yi+yi+yi+s
(At)a
c) Row reduce the augmented matrix [A[b] in b) and convert it into Echolon form (upper triangular form
in this case too.) and solve using Backward substitution
d) Write a Matlab script that can generate the A matrix and the b vector and solves for the position of
the ball at the time intervals [0.25, 0.50, 0.75, 1.00,..., 2.75] and plot t vs y
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