A hand-held calculator will suffice for this problem, where an initial value problem and its exact solution are given. Apply the Runge-Kutta method to approximate this solution on the interval [0, 0.5] with step size h = 0.25. Construct a table showing five-decimal-place values of the approximate solution and actual solution at the points x = 0.25 and 0.5. y' =y - 4x-4, y(0) = 7; y(x) = 8 + 4x - ex X 0 0.25 0.5 y with h = 0.25 7.00000 Actual y 7.00000 (Round to five decimal places as needed.)
A hand-held calculator will suffice for this problem, where an initial value problem and its exact solution are given. Apply the Runge-Kutta method to approximate this solution on the interval [0, 0.5] with step size h = 0.25. Construct a table showing five-decimal-place values of the approximate solution and actual solution at the points x = 0.25 and 0.5. y' =y - 4x-4, y(0) = 7; y(x) = 8 + 4x - ex X 0 0.25 0.5 y with h = 0.25 7.00000 Actual y 7.00000 (Round to five decimal places as needed.)
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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![A hand-held calculator will suffice for this problem, where an initial value problem and its
exact solution are given. Apply the Runge-Kutta method to approximate this solution on the
interval [0, 0.5] with step size h = 0.25. Construct a table showing five-decimal-place values
of the approximate solution and actual solution at the points x = 0.25 and 0.5.
y' =y - 4x-4, y(0) = 7; y(x) = 8 + 4x - ex
X
0
0.25
0.5
y with h = 0.25
7.00000
Actual y
7.00000
(Round to five decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3200e892-7b83-4670-8aa5-c4c84f2a6adb%2F5853e6bc-ac7e-446d-ba5b-9655fa916c20%2Fpxp7l4b_processed.png&w=3840&q=75)
Transcribed Image Text:A hand-held calculator will suffice for this problem, where an initial value problem and its
exact solution are given. Apply the Runge-Kutta method to approximate this solution on the
interval [0, 0.5] with step size h = 0.25. Construct a table showing five-decimal-place values
of the approximate solution and actual solution at the points x = 0.25 and 0.5.
y' =y - 4x-4, y(0) = 7; y(x) = 8 + 4x - ex
X
0
0.25
0.5
y with h = 0.25
7.00000
Actual y
7.00000
(Round to five decimal places as needed.)
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