Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first, third and last row. Box the final answer. No rounding off computed values. (x³ + y)dx – dy = 0 y(0) = 1
Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler method, b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first, third and last row. Box the final answer. No rounding off computed values. (x³ + y)dx – dy = 0 y(0) = 1
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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Please answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE.
I already have the final answer for the problem. I just need the complete and step-by-step process/solution on how it arrived to the final answer.
This topic falls under Numerical Methods.
Transcribed Image Text:a) Euler Method
Xn
Yn
0.0
1
1
0.5
1.5000
2
1.0
2.3125
1.5
3.9688
4
2.0
7.6406
2.5
15.4609
3.0
31.0039
b) Improved Euler Method
п
Xn
Уп
k1
k2
0.0
1.0000
0.5000
0.8125
1
0.5
1.6563
0.8906
1.7734
1.0
2.9883
1.9941
4.1787
3
1.5
6.0747
4.7249
9.3998
4
2.0
13.1370
10.5685
19.6653
2.5
28.2539
21.9395
38.5967
3.0
58.5220
c) 4th order Runge-Kutta Method
n
Xn
Уп
k1
k2
k3
k4
0.0
1.0000
0.5000
0.6328
0.6660
0.8955
1
0.5
1.6655
0.8953
1.2675
1.3606
2.0131
2
1.0
3.0263
2.0131
2.9930
3.2379
4.8196
3
1.5
6.2421
4.8085
7.0028
7.5514
10.8967
4
2.0
13.7110
10.8555
15.2647
16.3670
22.8515
2.5
29.8728
22.7489
31.0220
33.0903
44.9815
3.0
62.5319
LO CO
Transcribed Image Text:Using h = 0.5, approximate the value of y(3) for the given differential equation using a) Euler method,
b) Improved Euler method, and c) 4th order Runge-Kutta method. Show your solutions for the first,
third and last row. Box the final answer. No rounding off computed values.
(x³ + y)dx – dy = 0
y(0) = 1
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