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Solving integral equation with double ingegrals and singularities

  1. Oct 27, 2011 #1
    Hello
    I need help to solve the following integral equation:
    f(x,y,w)=137.03.*y.^2./((0.238.*exp(0.067.*y.^2)+1).*(w-5.26.*x.*y-2.63).*(w-5.26.*x.*y+2.63))=1+8478./(10828-w.^2-1.13.*j.*w)
    xmin=-1, xmax.=1, ymin=0, ymax=inf (nad can be taken 500 because the function decreases rapidly)
    I want to find w which is complex number.
    I tried the following code:
    f=@(w) dblquad(@(x,y) 137.03.*y.^2./((0.238.*exp(0.067.*y.^2)+1).*(w-5.26.*y.*x-2.63).*(w-5.26.*y.*x+2.63)),-1,1,0,100)-1-8478./(10828-w.^2-j.*w.*1.13)
    V=fsolve(f,160)
    There are some singularities. How can I solve the problem
     
  2. jcsd
  3. Oct 27, 2011 #2
    Looks like you have:

    [tex]g(w)=\int\int f(w,x,y)dxdy[/tex]

    for complex w. Then unless someone can suggest an analytical approach, I would recommend a brute-force search in the complex plane for w. Start with a circle about the origin. Say 100 points around it. Compute both sides. Find the minimum absolute value of the difference between the RHS and LHS. That the current point. Now take a small circle around that point, another 100 points, find the minimum again. Keep doing this and I think the trajectory will lead to the solution unless some problems are encountered.
     
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