Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's explicit method. with h=0.4. The analytical solution of the ODE is: y = x + Ze-x-1.In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
Consider the following first-order ODE: x-y from x 0 tox 1.2 with y(0) -1 dx Solve using Euler's explicit method. with h=0.4. The analytical solution of the ODE is: y = x + Ze-x-1.In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined.
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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![Consider the following first-order ODE:
x-y from x0 tox
1.2 with y(0) - 1
dz
Solve using Kuler's explicit method.with h = 0.4.
The analytical solution of the ODE is: y=x+2e-1. In each part, calculate the error between the true solution and the
numerical solution at the points where the numerical solution is determined.
X
0
0.4
0.8
1.2
1
0.4
0.52
0.928
error
0
0.2976 0.2824
0.202
X
0
0.4
0.8
1.2
y
1
0.5
0.5
0.75
error
0
0.2131 0.2358
0.196
X
0
0.4
0.8
1.2
y
1
0.6
0.52
0.632
error
0
0.1406
0.1787
0.170
None of the choices](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea932f5b-5387-46f1-b181-91f677d846f2%2Fb21c3dab-6e9b-42c8-ab47-0633475e8557%2Fad0jzcp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following first-order ODE:
x-y from x0 tox
1.2 with y(0) - 1
dz
Solve using Kuler's explicit method.with h = 0.4.
The analytical solution of the ODE is: y=x+2e-1. In each part, calculate the error between the true solution and the
numerical solution at the points where the numerical solution is determined.
X
0
0.4
0.8
1.2
1
0.4
0.52
0.928
error
0
0.2976 0.2824
0.202
X
0
0.4
0.8
1.2
y
1
0.5
0.5
0.75
error
0
0.2131 0.2358
0.196
X
0
0.4
0.8
1.2
y
1
0.6
0.52
0.632
error
0
0.1406
0.1787
0.170
None of the choices
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