Consider the differential equation with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) ~ 2 (Be sure not to round your calculations at each step!) Now use four steps: y(1)~ 0 (Be sure not to round your calculations at each step!) Magnitude of error in Euler with 2 steps = dy B. What is the solution to this differential equation (with the given initial condition)? y = 3x²+2 Magnitude of error in Euler with 4 steps = da C. What is the magnitude of the error in the two Euler approximations you found? 32 34 = 6x, D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor= (How close to this is the result you obtained above?)
Consider the differential equation with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) ~ 2 (Be sure not to round your calculations at each step!) Now use four steps: y(1)~ 0 (Be sure not to round your calculations at each step!) Magnitude of error in Euler with 2 steps = dy B. What is the solution to this differential equation (with the given initial condition)? y = 3x²+2 Magnitude of error in Euler with 4 steps = da C. What is the magnitude of the error in the two Euler approximations you found? 32 34 = 6x, D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)? factor= (How close to this is the result you obtained above?)
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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I just need the second part of A and D, thank you
Transcribed Image Text:Consider the differential equation
with initial condition y(0) = 2.
A. Use Euler's method with two steps to estimate y when x = 1:
y(1) ~ 2
(Be sure not to round your calculations at each step!)
Now use four steps:
y(1) ~
(Be sure not to round your calculations at each step!)
dy
da
B. What is the solution to this differential equation (with the given initial condition)?
y = 3x² + 2
Magnitude of error in Euler with 2 steps =
= 6x,
C. What is the magnitude of the error in the two Euler approximations you found?
3
2
Magnitude of error in Euler with 4 steps =
3
4
D. By what factor should the error in these approximations change (that is, the error with two steps should be what number times the error with four)?
factor =
(How close to this is the result you obtained above?)
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