- #1
leopard
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Homework Statement
We want to solve the equation
[tex]u_{xx}(x,y) + u_{yy}(x,y) = xu(x,y) [/tex]
on the square [0,1]x[0,1] with boundary conditions
u(x,0) = x
u(x,1) = x
u(0,y) = 0
u(1,y) = 1
Let h = 1/3 be the mesh. Set up a system of equations for [tex]u_{1,1}, u_{2,1}, u_{1,2}[/tex] and [tex]u_{2,2}[/tex]
2. The attempt at a solution
First point (1/3, 1/3):
-4[tex]u_{1,1}[/tex] + [tex]u_{2,1}[/tex] + [tex]u_{1,2}[/tex] = -x + x[tex]u_{1,1}[/tex]
This can be written
-13/3[tex]u_{1,1}[/tex] + [tex]u_{2,1}[/tex] + [tex]u_{1,2}[/tex] = -1/3
The correct equation for this point is
-109[tex]u_{1,1}[/tex] + 27[tex]u_{2,1}[/tex] + 27[tex]u_{1,2}[/tex] = -9
What is wrong?
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