Use the Runge-Kutta method to approximate x(0.2) and y(0.2). First use h = 0.2 and then use h 0.1. (Round your answers to four decimal places.) x' = x + 2y y' = 4x + 3y x(0) = 1, y(0) = 1 (x(0.2), y(0.2)) 1 (x(0.2), x(0.2), y(0.2)) ≈ ( Use a numerical solver and h (h = 0.2) |) (h = 0.1) = 0.1 to graph the solution in a neighborhood of t = 0. 3 2.0 1.5 x(t) y(t) 1.0 0.5 x(t) y(t) 0.05 0.10 0.15 t 0.20 0.05 0.10 0.15 0.20 t
Use the Runge-Kutta method to approximate x(0.2) and y(0.2). First use h = 0.2 and then use h 0.1. (Round your answers to four decimal places.) x' = x + 2y y' = 4x + 3y x(0) = 1, y(0) = 1 (x(0.2), y(0.2)) 1 (x(0.2), x(0.2), y(0.2)) ≈ ( Use a numerical solver and h (h = 0.2) |) (h = 0.1) = 0.1 to graph the solution in a neighborhood of t = 0. 3 2.0 1.5 x(t) y(t) 1.0 0.5 x(t) y(t) 0.05 0.10 0.15 t 0.20 0.05 0.10 0.15 0.20 t
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 the Runge-Kutta method to approximate x(0.2) and y(0.2). First use h = 0.2 and then use h 0.1. (Round your answers to four decimal places.)
x' = x + 2y
y' = 4x + 3y
x(0) = 1, y(0) = 1
(x(0.2), y(0.2)) 1
(x(0.2),
x(0.2), y(0.2)) ≈ (
Use a numerical solver and h
(h = 0.2)
|)
(h = 0.1)
= 0.1 to graph the solution in a neighborhood of t = 0.
3
2.0
1.5
x(t)
y(t)
1.0
0.5
x(t)
y(t)
0.05
0.10
0.15
t
0.20
0.05
0.10
0.15
0.20
t
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