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Laplace inverse transform

  1. Sep 25, 2004 #1
    Let,s suppose we want to get the inverse Laplace transform of a function f(s) numerically,we should calculate the integral from (c-i8,c+i8) of exp(st)f(s) my question is what c we should choose for calculating the integral?..wouldn,t depend the integral of the value of c..where could i find the proof that the Inverse Laplace transform does not depend on the value of c chosen?..

    Another question,let,s take the Laplace transform in 2 dimensions hten how would we define the Laplace inverse transform?..
  2. jcsd
  3. Sep 25, 2004 #2
    you can use the complexe analysis and résidue theorem
  4. Sep 26, 2004 #3
    but what would happen if i try solving it numerically for example we should calculate the integral over all R of exp(ixt)f(c+ix)exp(ct) and this would be equal to our inverse Laplace transform, the problem is what c would i choose?..thanx.
  5. Sep 28, 2004 #4
    So you have a complex integral (the integral of the inverse Laplace is a line integral in complex analysis) .
    It is impossible to calculate numerically these integral , because it is a line complex integral and not a simple integral like the reel integral , for this (if you know the complex analysis) their is an important theorem to calculate the value of the complex integral it is : Residue theorem, so use this theorem
  6. Sep 28, 2004 #5
    But making the change of variable c+iu the integral becomes simply a Fourier inverse transform (is a integral on the real plane of exp(iu)f(c+iu)exp(ct)) so if we can have a real integral and should be able to compute it numerically.
  7. Sep 29, 2004 #6
    It is wrong
    When you change the variale c+iu=v , so u change an COMPLEX variable and not a real variable!
  8. Sep 29, 2004 #7
    but the Laplace inverse transform is not just a special case of fourier transform?
  9. Sep 30, 2004 #8
    the Laplace inverse transform is not just a special case of fourier transform
    But when we calculate the Laplace we use the complexe variables and not the real variables
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