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 13m answered How to handle a special Neumann-like boundary condition in NDSolve? 19h answered Error propagation code 23h comment NDSolve: problem due to boundary conditions Just tried ep=zb=10^-4, though some warning pops up, the "shape" of result looks quite similar to that with ep=zb=10^-2, what's the unexpected part?: i.stack.imgur.com/aw0xw.png 23h comment Differential equations with rational functions as solution Write the solution out in terms of unknown coefficients, substitute, expand and collect terms, and solve the resulting system of equations is the only approach I can think out, and I think it should work when the degree isn't too high. Can you show an example that is hard to handle with this approach? 23h comment NDSolve: problem due to boundary conditions Can you show a concrete example for the numerical errors? Have you tried a higher WorkingPrecision? 1d comment Partial differential equation with infinity limit Is it - D[U0[t], t] or + D[U0[t], t]? And where's the initial condition ($u(y,0)=?$)? 1d revised How do I solve a PDE with a strange boundary condition? added 26 characters in body 2d comment Can't clear variables with subscripts 2d comment Table with List iterator return unpacked list Interesting, another possible evidence: With[{xx = Range[1., 10., 0.01]}, Table[w + ky, {w, Range[1., 10., 0.01]}, {ky, xx}]] // DeveloperPackedArrayQ 2d comment Table with List iterator return unpacked list Mathematica never promised to give you a packed array :D, anyway, it's a interesting observation. Feb 8 comment How to define a complicated function inside the body of Compile? @MichaelE2 Yeah, actually the memory cost is the only thing in my mind, because I think that's what OP is concerned. However, after checking FullForm@f, I noticed my answer is incorrect, it also inserts 3 copies of the (compiled) function into the body! So far I can't think out a way to define a sub routine as OP desires… Feb 7 comment How to define a complicated function inside the body of Compile? @MichaelE2 I guess it… depends on how the big nasty function is defined :D Feb 7 comment Weird behaviour for a vector InterpolatingFunction inside an NDSolve @march is right, {0} + g[x] will evaluate to {g[x]} before NDSolve execute. I think you'll find this post interesting: mathematica.stackexchange.com/a/97006/1871 Feb 7 answered How to define a complicated function inside the body of Compile? Feb 7 comment How to define a complicated function inside the body of Compile? I think this has little difference with define bigNastyFunction outside and use option "InlineExternalDefinitions" -> True, because then three copies of that function will be inserted into the body of the compiled function verbatim" Feb 2 revised Partial Differential Equation in Parallel edited tags Feb 2 revised Problems when solving a nonlinear PDE system with NDSolve deleted 1 character in body Feb 1 revised Problems when solving a nonlinear PDE system with NDSolve added 262 characters in body Feb 1 comment Problems when solving a nonlinear PDE system with NDSolve "Is there any offline version of such conversion tools", check this post:mathematica.stackexchange.com/q/1137/1871 . As to your new update, since I'm now at home and have no access to the new mentioned article, I'd like to stop verifying the model, I write this comment mainly to mention, the NDSolve::bcart: can be suppressed by using T[x, 0] == (Tw - Tgin) (Exp[1000 (x - xr)]) + Tgin instead of the corresponding boundary, NDSolve::pdord can be suppressed by using neweq5 = D[sys[[5]], t] /. Solve[D[sys[[4]], t], Derivative[0, 2][Tg][x, t]][[1]];  instead of eq5`. Jan 30 comment Problems when solving a nonlinear PDE system with NDSolve BTW, I usually use steampiano.net/msc to convert the special characters. halirutan's extension is quite unstable at least in my Chrome.