Re: InverseLaplaceTransform

*To*: mathgroup at smc.vnet.net*Subject*: [mg26681] Re: InverseLaplaceTransform*From*: Roland Franzius <Roland.Franzius at uos.de>*Date*: Wed, 17 Jan 2001 00:47:30 -0500 (EST)*Organization*: Universitaet Osnabrueck*References*: <93ramm$57u@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Knut Henning Schroder wrote: > > I try to find a symbolic solution of: > InverseLaplaceTransform[(s + a)/(b s Sqrt[s] + c Sqrt[s] + d), s, t] > for electrode processes in electrochemistry. Can you help me? > Thank you and regards, > Knut Schroder You may perform a partial fraction decomposition of the denominator in the variable x=Sqrt[s]. Then, you get a linear combination of functions s/(Sqrt[s]-A), a * 1/(Sqrt[s]-A) and something similar for the other zeros B,C of b x^3 + c x + d ==0. The inverse LaplaceTransform of the simple terms are InvLap[1/(Sqrt[s]-A),s,t] = f[t] = 1/Sqrt[Pi t] A e^(A^2 t) Erfc[A Sqrt[t]] InvLap[s/(Sqrt[s]-A),s,t] = -d/dt f[t] Hope it helps regards -- Roland Franzius +++ exactly <<n>> lines of this message have value <<FALSE>> +++