2. Use the (a) Euler and (b) Heun (without iteration) methods to solve d'y -t+y=0 dt2 where y(0)-2 and y'(0)-0. Solve from x-0 to 4 using h-0.1. Compare the methods by plotting the solutions. The second-order ODE is transformed into a pair of first-order ODEs as in dt dz dt t-y y(0)-2 z(0)-0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 47RE
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Question
2. Use the (a) Euler and (b) Heun (without iteration) methods to solve
d'y
-t+y=0
dt²
where y(0) = 2 and y(0)=0. Solve from x-0 to 4 using h=0.1. Compare the methods by plotting the solutions.
The second-order ODE is transformed into a pair of first-order ODEs as in
dy
dt
dz
dt
2
=t-y
y(0)=2
z(0) 0
Transcribed Image Text:2. Use the (a) Euler and (b) Heun (without iteration) methods to solve d'y -t+y=0 dt² where y(0) = 2 and y(0)=0. Solve from x-0 to 4 using h=0.1. Compare the methods by plotting the solutions. The second-order ODE is transformed into a pair of first-order ODEs as in dy dt dz dt 2 =t-y y(0)=2 z(0) 0
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