Consider the following first-order ODE: dy 4e0.8x – 0.5y, x = [0, 1], y(x = 0) = 2 %3D dx The analytical solution of this equation is determined, as follows: 4 (e0.8x – e-0.5x) + 2e 1.3 -0.5x У (х) - Using step size h = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decin %3D places) Yi Yi Yi (Analytical, Xi (Predictor, (Corrector, from Error Euler's) Heun's) analytical solution) 0. 0. 1 0.25 0.50 3 0.75 4. 1.00
Consider the following first-order ODE: dy 4e0.8x – 0.5y, x = [0, 1], y(x = 0) = 2 %3D dx The analytical solution of this equation is determined, as follows: 4 (e0.8x – e-0.5x) + 2e 1.3 -0.5x У (х) - Using step size h = 0.25, fill-up the following table using indicated methods (table entries should be expressed in 5 decin %3D places) Yi Yi Yi (Analytical, Xi (Predictor, (Corrector, from Error Euler's) Heun's) analytical solution) 0. 0. 1 0.25 0.50 3 0.75 4. 1.00
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
![Consider the following first-order ODE:
dy
4e0.8x – 0.5y,
dx
x = [0, 1], y(x = 0) = 2
The analytical solution of this equation is determined, as follows:
4
y (x) =
(e0.8x – e-0.5x) + 2e¬0.5x
1.3
Using step sizeh = 0.25, fill-up the following table using indicated methods
(table entries should be expressed in 5 decimal places)
%3D
Yi
Yi
Yi
(Analytical,
(Predictor,
(Corrector,
from
Error
Euler's)
Heun's).
analytical
solution)
1
0.25
2
0.50
3
0.75
4
1.00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F082cf058-8a03-4046-9945-1fc4a28c94dc%2F29facb01-7bfc-419d-b34f-16b7eb23ec04%2F74as35r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following first-order ODE:
dy
4e0.8x – 0.5y,
dx
x = [0, 1], y(x = 0) = 2
The analytical solution of this equation is determined, as follows:
4
y (x) =
(e0.8x – e-0.5x) + 2e¬0.5x
1.3
Using step sizeh = 0.25, fill-up the following table using indicated methods
(table entries should be expressed in 5 decimal places)
%3D
Yi
Yi
Yi
(Analytical,
(Predictor,
(Corrector,
from
Error
Euler's)
Heun's).
analytical
solution)
1
0.25
2
0.50
3
0.75
4
1.00
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