Use the RK4 method to approximate y(0.2), where y(x) is the solution of the initial-value problem y'' − 6y' + 9y = 0, y(0) = −4, y'(0) = 1. First use h = 0.2 and then use h = 0.1. Find the exact solution of the problem, and compare the actual value of y(0.2) with the approximated values. (Round your answers to four decimal places.) y(0.2) ≈ (h = 0.2) y(0.2) ≈ (h = 0.1) y(0.2) = (exact value)
Use the RK4 method to approximate y(0.2), where y(x) is the solution of the initial-value problem y'' − 6y' + 9y = 0, y(0) = −4, y'(0) = 1. First use h = 0.2 and then use h = 0.1. Find the exact solution of the problem, and compare the actual value of y(0.2) with the approximated values. (Round your answers to four decimal places.) y(0.2) ≈ (h = 0.2) y(0.2) ≈ (h = 0.1) y(0.2) = (exact value)
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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Use the RK4 method to approximate y(0.2), where y(x) is the solution of the initial-value problem
y'' − 6y' + 9y = 0, y(0) = −4, y'(0) = 1.
First use
h = 0.2
and then use
h = 0.1.
Find the exact solution of the problem, and compare the actual value of y(0.2) with the approximated values. (Round your answers to four decimal places.)
| y(0.2) ≈ |
(h = 0.2)
|
|
| y(0.2) ≈ |
(h = 0.1)
|
|
| y(0.2) = | (exact value) |
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