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. Use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Xn Yn Error 0.00 1.0000 1.0000 0.0000 0.00 0.10 1.1052 0.20 1.2214 0.30 1.3499 0.40 1.4918 0.50 1.6487 0.60 1.8221 0.70 2.0138 0.80 2.2255 0.90 2.4596 1.00 2.7183
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. Use the rounded values for subsequent calculations.) y' = y, y(0) = 1; y(1.0) y(x) = (explicit solution) h = 0.1 Actual Value Absolute % Rel. Error Xn Yn Error 0.00 1.0000 1.0000 0.0000 0.00 0.10 1.1052 0.20 1.2214 0.30 1.3499 0.40 1.4918 0.50 1.6487 0.60 1.8221 0.70 2.0138 0.80 2.2255 0.90 2.4596 1.00 2.7183
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. Use the rounded values for subsequent calculations.)
У'%3D у, у(0) %3D 1; у(1.0)
У(x) %3
(explicit solution)
h = 0.1
Xn
Yn
Actual
Absolute
% Rel.
Value
Error
Error
0.00
1.0000
1.0000
0.0000
0.00
0.10
1.1052
0.20
1.2214
0.30
1.3499
0.40
1.4918
0.50
1.6487
0.60
1.8221
0.70
2.0138
0.80
2.2255
0.90
2.4596
1.00
2.7183
Transcribed Image Text:h = 0.05
Xn
Yn
Actual
Absolute
% Rel.
Value
Error
Error
0.00
1.0000
1.0000
0.0000
0.00
0.05
1.0500
1.0513
0.0013
0.12
0.10
1.1025
1.1052
0.0027
0.24
0.15
1.1576
1.1618
0.0042
0.36
0.20
1.2155
1.2214
0.0059
0.48
0.25
1.2763
1.2840
0.0077
0.60
0.30
1.3401
1.3499
0.0098
0.73
0.35
1.4071
1.4191
0.0120
0.85
0.40
1.4775
1.4918
0.0143
0.96
0.45
1.5514
1.5683
0.0169
1.08
0.50
1.6290
1.6487
0.0197
1.19
0.55
1.7105
1.7333
0.0228
1.32
0.60
1.7960
1.8221
0.0261
1.43
0.65
1.8858
1.9155
0.0297
1.55
0.70
1.9801
2.0138
0.0337
1.67
0.75
2.0791
2.1170
0.0379
1.79
0.80
2.1831
2.2255
0.0424
1.91
0.85
2.2923
2.3396
0.0473
2.02
0.90
2.4069
2.4596
0.0527
2.14
0.95
2.5272
2.5857
0.0585
2.26
1.00
2.7183
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