Find the smallest (in absolute value) eigenvalue using
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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Hi hope for clear and understandable hand writing
![(а)
Given
-1 2
3
A =| 2 1 -1
1 -1
-1 1
4
Find the smallest (in absolute value) eigenvalue using inverse power method. Take
y0) = [0 1 1].
(b)
ди
Given the heat equation
0<x< 4, t > 0 with the boundary conditions
u(0,t) = 1² Int and u(4,t) = r² for t>0
and the initial conditions,
х,
0<x< 2,
и (х.0) -
(4-x, 2<x< 4.
By taking h = Ax = 1, k = At = 0.2 and a =1, solve the heat equation up to second
level using implicit Crank-Nicolson method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ff0dd7-5074-4aec-9066-90442c8994e4%2Fb6cca25c-a0d0-415c-b9df-9146ca96851c%2Fjgyuje_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(а)
Given
-1 2
3
A =| 2 1 -1
1 -1
-1 1
4
Find the smallest (in absolute value) eigenvalue using inverse power method. Take
y0) = [0 1 1].
(b)
ди
Given the heat equation
0<x< 4, t > 0 with the boundary conditions
u(0,t) = 1² Int and u(4,t) = r² for t>0
and the initial conditions,
х,
0<x< 2,
и (х.0) -
(4-x, 2<x< 4.
By taking h = Ax = 1, k = At = 0.2 and a =1, solve the heat equation up to second
level using implicit Crank-Nicolson method.
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