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
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Chapter2: Second-order Linear Odes
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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
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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