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Laplace Equation in a square

  1. May 12, 2014 #1
    1. The problem statement, all variables and given/known data

    i need to solve the laplace equation in square with lenght side 1 i tried to solve by superposition and i got infinite sum enen thouth i know that the answer should be finite

    2. Relevant equations

    1.ψ(x=0,0≤y≤1)=0
    2.ψ(y=0,0≤x≤1)=0
    3.ψ(x=1,0≤y≤1)=10sin(∏*y)+3x
    4.ψ(y=1,0≤x≤1)=9sin(2∏*y)+3x

    3. The attempt at a solution
    from 1 and to 2 have (by superposition):
    ψ n=Asin(n∏x)sinh(n∏y) or ψ n=Asin(n∏y)sinh(n∏x)
    and after multiply by sin(n∏x)
    A n=2∫((9sin(2∏x)+3x)*sin(n∏x))/sinh(n∏) (the integral from 0 to 1)
    the problem is that i heve the infinite sum from ∫3x*sin(n∏x)
    thank you very much!
     
  2. jcsd
  3. May 12, 2014 #2

    BvU

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    Hello cg, and welcome to PI.
    Are you sure your relevant equations are relevant equations ? They look like boundary conditions to me.
    In that case, filling in x=1 changes 10sin(∏*y)+3x to 10sin(∏*y)+3 and 9sin(2∏*y)+3x changes into 3x.
    And then the relevant eqations still have to be found out ....
     
  4. May 13, 2014 #3
    hi BvU and thanks.
    you were right this is boundry conditions and they are also incorrect (i am sorry)
    3.ψ(x=1,0≤y≤1)=10sin(∏*y)+3y
    4.ψ(y=1,0≤x≤1)=9sin(2∏*x)+3x
     
  5. May 13, 2014 #4

    BvU

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    And then the relevant eqations still have to be found out .... What do you have available ?
     
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