Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing values of the approximate solution and the actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5. y' = - y, y(0) = 1; y(x) = ex Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.9048 0.8187 0.7408 0.6703 30.6065 0.5
Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h = 0.1. Construct a table showing values of the approximate solution and the actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5. y' = - y, y(0) = 1; y(x) = ex Complete the table below. (Round to four decimal places as needed.) Xn Actual, y (xn) Improved Euler, yn 0.1 0.2 0.3 0.4 0.9048 0.8187 0.7408 0.6703 30.6065 0.5
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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![Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with
step size h = 0.1. Construct a table showing values of the approximate solution and the
actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5.
y' = -y, y(0) = 1; y(x) = e¯X
Complete the table below.
(Round to four decimal places as needed.)
Xn
Actual, y (xn)
Improved Euler, yn
0.1
0.9048
0.2
0.3
0.4
0.8187 0.7408 0.6703
0.5
0.6065](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3200e892-7b83-4670-8aa5-c4c84f2a6adb%2F039ba663-0952-455f-aea0-7ad48779e2cf%2Fpayq1wgh_processed.png&w=3840&q=75)
Transcribed Image Text:Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with
step size h = 0.1. Construct a table showing values of the approximate solution and the
actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5.
y' = -y, y(0) = 1; y(x) = e¯X
Complete the table below.
(Round to four decimal places as needed.)
Xn
Actual, y (xn)
Improved Euler, yn
0.1
0.9048
0.2
0.3
0.4
0.8187 0.7408 0.6703
0.5
0.6065
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