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MathGroup Archive 2007

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Re: numerical inversion of laplace transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74946] Re: numerical inversion of laplace transform
  • From: "Roman" <rschmied at gmail.com>
  • Date: Thu, 12 Apr 2007 04:51:59 -0400 (EDT)
  • References: <evfk8c$5bk$1@smc.vnet.net><evhu8p$32n$1@smc.vnet.net>

Dan,

Given your G(t), what I wrote can be simplified drastically. First,
transform to exponential writing using
   TrigToExp[G[t]]
Then, you can manually do the transformation I wrote at 3) on the
prefactors of the exponentials. For example, the term with Exp[-i*Pi*t/
84], which has w=Pi/84, acquires an extra factor of -i*w/(1-
Exp[i*w*a]) = 0.0257383 - 0.0187*i. The constant term gets a prefactor
of 1/a.

Putting everything together, you get

F[t] = 303/(50*a)
  - Cos[(Pi*t)/84]*((59*Pi)/3360 + (139*Pi*Cot[(a*Pi)/168])/5600)
  + Cos[(Pi*t)/42]*((71*Pi)/8400 + (17*Pi*Cot[(a*Pi)/84])/1200)
  + ((139*Pi)/5600 - (59*Pi*Cot[(a*Pi)/168])/3360)*Sin[(Pi*t)/84]
  - ((17*Pi)/1200 - (71*Pi*Cot[(a*Pi)/84])/8400)*Sin[(Pi*t)/42]

With a = 33.6 as you specify, you get

F[t] = 0.18035714285714283
  - 0.16249350579592095*Cos[(Pi*t)/84]
  + 0.04101478009014459*Cos[(Pi*t)/42]
  + 0.0020508865613427935*Sin[(Pi*t)/84]
  - 0.035877998487864125*Sin[(Pi*t)/42]

Roman.

On Apr 11, 8:12 am, "dantimatter" <dantimat... at gmail.com> wrote:
> hi dimitris,
>
> sorry about that posting.  here we go again:
>
> G(t)=6.06 - 4.17*Cos[(Pi*t)/84] + 1.19*Cos[(Pi*t)/42] -
> 2.95*Sin[(Pi*t)/84] + 0.71*Sin[(Pi*t)/42]
> p(t) = UnitStep[33.6 - t]
>
> so that the Laplace-transformed function that I'd like to invert, G(s)/
> p(s) is
>
> G(s)/p(s) =
> (3.83*^7*E^(33.6*s)*(0.0029 - 0.049*s + s^2)*(0.0054 + 0.031*s + s^2))/
> ((-1. + E^(33.6*s))*(Pi^2 + 1764.*s^2)*(Pi^2 + 7056.*s^2))
>
> thanks!
> dan




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