3. Elliptic equation. Given the harmonic Laplace function u(x,y) in the rectangle R = {(x,y): 0≤x≤ 3,0 ≤ y ≤3}. The boundary values are u(x, 3) = 80 and u(0, y) = 40 and The grid is given as a. 11,3 11,2 112,4 95 ● 93 u₁(x,0)=130 u(3,y)=10 U13,4 96 94 for 0

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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3. Elliptic equation. Given the harmonic Laplace function u(x,y) in the rectangle R = {(x,y): 0≤x≤
3,0 ≤ y ≤3}. The boundary values are
The grid is given as
u(x,3)=80 and u₁(x,0)=130
u(0, y) = 40
and
u(3,y)=10
U13,4
1₁.3
141,2
U₁1
U2,4
●
95
93
96
94
for 0<x<3,
for 0 ≤ y <3.
U 4.3
114.2
U 4,1
9₁
92
a. Determine the system of six equations in the six unknowns 9₁, 92,
approximation.
b. Solve the equations in (a) for 9₁, 92, ..., 96. Use Gauss-Jordan Method.
96 to compute the
Transcribed Image Text:3. Elliptic equation. Given the harmonic Laplace function u(x,y) in the rectangle R = {(x,y): 0≤x≤ 3,0 ≤ y ≤3}. The boundary values are The grid is given as u(x,3)=80 and u₁(x,0)=130 u(0, y) = 40 and u(3,y)=10 U13,4 1₁.3 141,2 U₁1 U2,4 ● 95 93 96 94 for 0<x<3, for 0 ≤ y <3. U 4.3 114.2 U 4,1 9₁ 92 a. Determine the system of six equations in the six unknowns 9₁, 92, approximation. b. Solve the equations in (a) for 9₁, 92, ..., 96. Use Gauss-Jordan Method. 96 to compute the
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