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Integrla equation

  1. Sep 14, 2005 #1
    Let be the integral equation:

    [tex]\int_{a}^{b}dyK(x,y)f(y)=g(x)[/tex]where f is unknown and g is known, then i use a resolvent Kernel in the form:

    [tex]\int_{a}^{b}dyR(x,y)g(y)=f(x) [/tex] where we obtain the Kernel R by:

    [tex]R=\sum_{n=0}^{\infty}b_{n}(K-I)^{n}[/tex] the last is Neumann series for the Kernel operator R..is my approach always true?..thanks.
     
  2. jcsd
  3. Sep 14, 2005 #2

    HallsofIvy

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    Yes, that will work. It's a bit tedious in some cases.
     
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