bad PDE solution...

*To*: mathgroup at smc.vnet.net*Subject*: [mg129440] bad PDE solution...*From*: Fred Bartoli <""@news.free.fr>*Date*: Mon, 14 Jan 2013 00:03:10 -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*Reply-to*: myname_with_a_dot_inbetween at free.fr

Hello, As a first simple test case of a more complicated pb I want to solve the plane diffusion equation. It seems NDSolve gives a bad answer to the simple step case but I can't find what's happening... (* Set up the equation: *) eq1=D[h[t,x],x,x]- k1 D[h[t,x],t]==0 const=k1-> 10000 (*"solve" it...*) sol = NDSolve[ {D[h[t, x], {x, 2}] - k1 D[h[t, x], t] == 0, h[0, x] == 0, h[t, 1] == 0, h[t, 0] == 1 - Exp[-10^6*t]} /. const, h, {t, 0, 10^-3}, {x, 0, 0.01}][[1]] Plot3D[(h[t,x])/.mag/.solCart,{x,0,10^-4},{t,0,10^-4},AxesLabel->{"x","t","h"},PlotRange->All,PlotLabel->"Bogus solution"] Plot3D[Erfc[x/(2*Sqrt[t/k1])]/.const,{x,0,10^-4},{t,0,10^-4},AxesLabel->{"X","t","h"},PlotRange->All,PlotLabel->"The right one"] (* Test the Erfc[x/(2Sqrt[t/k1])] solution *) Release[Hold[D[h[t,x],x,x]- k1*D[h[t,x],t]]/. h[t,x]->Erfc[x/(2*Sqrt[t/k1])]]//Simplify I hope I'm doing something wrong, but I can find what... -- Thanks, Fred.