Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98
Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98
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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Transcribed Image Text:Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four
decimal places. Percentages may be rounded to two decimal places.)
y' = 2xy, y(1) = 1; y(1.5)
(explicit solution)
y(x) =
Xn
1.00
1.10
1.20
1.30
1.40
1.50
Xn
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
Yn
1.0000
Yn
1.0000
1.1000
1.2155
1.3492
1.5044
1.6849
1.8955
2.1419
2.4311
2.7715
h = 0.1
Actual
Value
1.0000
1.2337
1.5527
1.9937
2.6117
3.4903
h = 0.05
Actual
Value
1.0000
1.1079
1.2337
1.3806
1.5527
1.7551
1.9937
2.2762
2.6117
3.0117
3.4903
Absolute
Error
0.0000
Absolute
Error
0.0000
0.0079
0.0182
0.0314
0.0483
0.0702
0.0982
0.1343
0.1806
0.2402
% Rel.
Error
0.00
00000
% Rel.
Error
0.00
0.71
1.48
2.27
3.11
4.00
4.93
5.90
6.92
7.98
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