The application of a finite-difference scheme to the heat equation on a three-point grid results in the following system of equations: u+¹=[A]u where 0 i] T and r= a^t/(Ax)². Determine the stability of this scheme. [A]= 10 1-2r 0 0 1
The application of a finite-difference scheme to the heat equation on a three-point grid results in the following system of equations: u+¹=[A]u where 0 i] T and r= a^t/(Ax)². Determine the stability of this scheme. [A]= 10 1-2r 0 0 1
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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![The application of a finite-difference scheme to the heat equation on a three-point
grid results in the following system of equations:
u₁+¹=[A]u
where
TAJ-|
and r= a^t/(Ax)². Determine the stability of this scheme.
1
ľ
0
1-2r T
0 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0e55c35-c186-467f-9f9f-aa82bdc5660a%2F57c3a0dc-a033-4d74-a238-cdb745cd52e9%2Fuvpke4e_processed.png&w=3840&q=75)
Transcribed Image Text:The application of a finite-difference scheme to the heat equation on a three-point
grid results in the following system of equations:
u₁+¹=[A]u
where
TAJ-|
and r= a^t/(Ax)². Determine the stability of this scheme.
1
ľ
0
1-2r T
0 1
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