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' = y₁ y(0)=1; y(1.0) y(x) = Xn 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Yn 1.0000 (explicit solution) h = 0.1 Actual Value 1.0000 1.1052 1.2214 1.3499 1.4918 1.6487 1.8221 2.0138 2.2255 2.4596 Absolute Error 0.0000 % Rel. Error 0.00
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' = y₁ y(0)=1; y(1.0) y(x) = Xn 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Yn 1.0000 (explicit solution) h = 0.1 Actual Value 1.0000 1.1052 1.2214 1.3499 1.4918 1.6487 1.8221 2.0138 2.2255 2.4596 Absolute Error 0.0000 % Rel. Error 0.00
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
2.6-2
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.)
y' = y, y(0) = 1; y(1.0)
y(x) =
Xn
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Xn
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Уп
1.0000
Уп
1.0000
1.0500
1.1025
1.1576
1.2155
1.2763
1.3401
1.4071
1.4775
1.5514
1.6290
1.7105
1.7960
1.8858
1.9801
2.0791
2.1831
2.2923
2.4069
2.5272
(explicit solution)
h = 0.1
Actual
Value
1.0000
1.1052
1.2214
1.3499
1.4918
1.6487
1.8221
2.0138
2.2255
2.4596
2.7183
h = 0.05
Actual
Value
1.0000
1.0513
1.1052
1.1618
1.2214
1.2840
1.3499
1.4191
1.4918
1.5683
1.6487
1.7333
1.8221
1.9155
2.0138
2.1170
2.2255
2.3396
2.4596
2.5857
2.7183
Absolute
Error
0.0000
Absolute
Error
0.0000
0.0013
0.0027
0.0042
0.0059
0.0077
0.0098
0.0120
0.0143
0.0169
0.0197
0.0228
0.0261
0.0297
0.0337
0.0379
0.0424
0.0473
0.0527
0.0585
% Rel.
Error
0.00
% Rel.
Error
0.00
0.12
0.24
0.36
0.48
0.60
0.73
0.85
0.96
1.08
1.19
1.32
1.43
1.55
1.67
1.79
1.91
2.02
2.14
2.26
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