What are the largest steps you take to solve -4y, y(0)=1 dt (without getting an overflow!) using the Forward Euler method? The backward Euler method? Would your answer change if you wanted the solution to always be positive? How?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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2) Stability for linear systems
(a) What are the largest steps you take to solve
dy
dt
-4y, y(0) = 1
(without getting an overflow!) using the Forward Euler method? The backward Euler method? Would your answer
change if you wanted the solution to always be positive? How?
(b) A linear system has the form
dy
di
y(0) = (1,0,0)
Suppose the eigenvalues of A are λ₁ = -1,22=-1/2+2i and 23 = -1/2-2i. What is the largest value of h you
could use to stably solve the problem with Forward Euler?
= Ay,
Transcribed Image Text:2) Stability for linear systems (a) What are the largest steps you take to solve dy dt -4y, y(0) = 1 (without getting an overflow!) using the Forward Euler method? The backward Euler method? Would your answer change if you wanted the solution to always be positive? How? (b) A linear system has the form dy di y(0) = (1,0,0) Suppose the eigenvalues of A are λ₁ = -1,22=-1/2+2i and 23 = -1/2-2i. What is the largest value of h you could use to stably solve the problem with Forward Euler? = Ay,
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