Separating space and time functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg130006] Separating space and time functions*From*: carlos%colorado.edu at gtempaccount.com*Date*: Sun, 3 Mar 2013 23:00:16 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

When solving certain spacetime PDEs I get a solution F that can be factored as F(space,time) = f(space)*g(time) E.g., in 1D space, F(x,y)= (a0+a1*x+a2*x^2)*(b0+b1*t+b2*Log[t]), which will be used as one of the test functions below. Then f(x)=a0+a1*x+a2*x^2 and g(t)=b0+b1*t+b2*Log[t]. I wrote the following module to separate g(t): SeparateFunctionOfTime[f_,t_]:=Module[{g1,g2,g}, g1=Simplify[D[f,t]/f]; g2=Simplify[Integrate[g1,t]]; g= Simplify[Exp[g2]]; Return[g]]; ClearAll[x,t,a0,a1,a2,b0,b1,b2]; f=(a0+a1*x+a2*x^2)*(b0+b1*t+b2*Log[t]); Print["sep time function: ", SeparateFunctionOfTime[f,t]]; sep time function: b0 + b1 t + b2 Log[t] (I typed all of the above code directly, looking at a test cell.) So far this has worked for the problems I have solved so far (I am doing wave dispersion studies in some advanced micromaterials). Questions: (1) could this method fail if Integrate[..] is unable to do the integrand f'/f = (Log[f])', and (2) could a more robust method be used then?