Consider the following first-order ODE: dy =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 dx Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x2 - 6x-6+; In each part, calculate the error between the true solution 8e0.5 and the numerical solution at the points where the numerical solution is determined.
Consider the following first-order ODE: dy =y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1 dx Solve using Euler's explicit method. (h= 0.4) 71e* The analytical solution of the ODE is: y=-x³-3x2 - 6x-6+; In each part, calculate the error between the true solution 8e0.5 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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Question
Transcribed Image Text:Consider the following first-order ODE:
dy
dx
=y+x³ from x = 0.5 to x = 2.1 1with y(0.5) = -1
Solve using Euler's explicit method. (h= 0.4)
71e*
The analytical solution of the ODE is: y=-x³-3x² - 6x-6+
8e0.5
and the numerical solution at the points where the numerical solution is determined.
X
0.5
0.9
1.3
y
-1
-1.35
-1.6
error
0
0.0309 0.2831
X
0.5
0.9
1.3
y
-1
-1.33
-1.38
error
0
0.0137 0.0665
X
0.5
0.9
1.3
y
-1
-1.32
-1.32
error
0
0
0.0002
None of the choices
In each part, calculate the error between the true solution
1.7
-1.36
1.042
1.7
-0.52
0.2024
1.7
-0.32
0.0008
2.1
0.0
2.8
2.1
2.3
0.4
2.1
2.8
0.0
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