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