Re: InverseLaplaceTransform different solution in Mathematica 6 and
- To: mathgroup at smc.vnet.net
- Subject: [mg94171] Re: InverseLaplaceTransform different solution in Mathematica 6 and
- From: dimitris <dimmechan at yahoo.com>
- Date: Sat, 6 Dec 2008 06:16:12 -0500 (EST)
- References: <gh8hnh$r3o$1@smc.vnet.net>
On 4 =C4=E5=EA, 14:16, Guillermo Sanchez <guillermo.sanc... at hotmail.com> wrote: > Dear friends, > Mathematica 6 gives the analytical right answer evaluating > InverseLaplaceTransform[E^((1 - Sqrt[1 + 4*d*(s + d*r)])/(2*d)), s, > t], > However Mathematica 7.0.0 does not the analytical solution. Is it a > bug? > > Guillermo Did you try to evaluate the inverse Laplace function for a specific value of d? Is d positive for example? I don't own version 6, let alone 7 but the following "trick" used to work in some older versions... In[254]:= E^((1 - Sqrt[1 + 4*d*(s + d*r)])/(2*d)) /. d -> Catalan InverseLaplaceTransform[%, s, t] % /. Catalan -> d Out[254]= E^((1 - Sqrt[1 + 4*Catalan*(Catalan*r + s)])/(2*Catalan)) Out[255]= E^(1/(2*Catalan) - 1/(4*Catalan*t) - t/(4*Catalan) - Catalan*r*t)/ (2*Sqrt[Catalan*Pi]*Sqrt[t^3]) Out[256]= E^(1/(2*d) - 1/(4*d*t) - t/(4*d) - d*r*t)/(2*Sqrt[d]*Sqrt[Pi]*Sqrt [t^3]) Regards Dimitris