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Dirichlet problem

  1. Nov 27, 2008 #1
    1. The problem statement, all variables and given/known data

    We wanna 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?
     
    Last edited: Nov 27, 2008
  2. jcsd
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