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Re: Can anyone help about this inverse laplace transform problem?

• To: mathgroup at smc.vnet.net
• Subject: [mg33279] Re: [mg33260] Can anyone help about this inverse laplace transform problem?
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Wed, 13 Mar 2002 03:14:49 -0500 (EST)
• Organization: JEOL (USA) Ltd.
• References: <200203121009.FAA13342@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

david Xia wrote:

> Hello,
>
>    I am a new user of Mathematica, and want to get the following inverse
> laplace transform problem:
>
>    I have 8 parameters, a,b,c,d,w1,w2,w3,w4. (Where there is a constrain
> that a+b+c+d=1)
>
>    The following is the script I tried.
> -------------------------------------------------------------
>    f4s=a w1/(s+a)+b w2/(s+b)+c w3/(s+c)+d w4/(s+d)
>    fi=f4s/(1-f4s)
>    InverseLaplaceTransform[fi,s,t]
> ----------------------------------------------------------------
>    I tried to run it, but mathematica runs forever and can not give me an
> answer. Can it be solved by Mathematica?
>
>    Any ideas?
>

I don't know why Mathematica doesn't return a result, but I played around a
little with your problem and have some suggestions.  Since your function is
rational and the denominator is of fourth degree you can calculate the poles
of the expression explicitly using Roots.  You can then perform the inverse
transform explicitly by taking the sum of the residues evaluated at the
poles.  This is a complicated expression.  Your constraint may allow you to
simplify a few of the terms.

Regards,

Sseziwa

• References:
  • Can anyone help about this inverse laplace transform problem?
    • From: "david Xia" <xiaxd@hotmail.com>