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 Apr21 revised BC for transport equation using NDSolve Improve the format Apr21 comment Solving coupled differential equations with an eigenvalue As mentioned above, ϕ[Ei] == 0 and ϕ'[Ei] == 0 give two equations, use either of them inside FindRoot or RootSearch will give you a result. Apr21 revised solve ODE with divergencies Improve the format Apr21 revised solve ODE with divergencies Improve the format. Apr21 revised solve ODE with divergencies Improve the format Apr21 comment Analogue for Maple's dchange - change of variables in differential expressions After playing with it a bit, I feel that writing one-element list is a little inconvenient. It'll be good if syntax like dChange[D[u[x, t], t] == D[u[x, t], {x, 2}], x == ξ s[t], x, ξ, u[x, t]] is supported. Not sure what's the standard way to implement this, though. (Something like {internalold, internalfun} = If[Head@# =!= List, {#}, #] & /@ {oldVars, functions} ?) Apr20 comment RegionPlot3D exponentiation issue [Mathematica 10] No, it's not empty, if you look carefully, you'll see one point at the origin, and it's the only point inside the region. Apr20 revised Analogue for Maple's dchange - change of variables in differential expressions added 2 characters in body Apr20 comment Analogue for Maple's dchange - change of variables in differential expressions Your design for the syntax is undoubtedly more Mathematica-like and more reasonable. (I admit that when writing the question I haven't deliberated on the syntax design. ) Apr18 awarded Nice Question Apr18 revised Analogue for Maple's dchange - change of variables in differential expressions grammar mistakes fixed Apr18 revised Analogue for Maple's dchange - change of variables in differential expressions add examples for expected behavior. Apr18 revised Analogue for Maple's dchange - change of variables in differential expressions added 4 characters in body Apr18 comment Analogue for Maple's dchange - change of variables in differential expressions @m0nhawk Well, as I mentioned above, that's just one of the related questions that are not general enough. Apr18 asked Analogue for Maple's dchange - change of variables in differential expressions Apr18 comment Integro differential eq boundary difficulties I suggest you to add the $LaTeX$ or screenshot of your original PDE to your question. BTW, a simple mistake is exp should be Exp. Apr18 comment NDSolve to solve a PDF "Numerically, using the method of lines (the default in this case), condition 1 is not integrated." Yeah, actually this has been (vaguely) mentioned in the possible issue of DiracDelta: Numerical routines will typically miss the contributions from measures at single points. Apr18 comment Solving coupled differential equations with an eigenvalue What approach do you want to take for finding Ei? b[Ei] actually returns 2 InterpolatingFunction while you only have 1 unknown! If you replace the {ϕ, A} inside ParametricNDSolve with ϕ or A, you'll get a solution, whether the solution is correct or not is another story. BTW, you may want to try this package: library.wolfram.com/infocenter/Demos/4482 Apr18 comment Nest-Recursion leads to overflow - Numerical calculation of Lyapunov exponents It's just an issue of error accumulation. Use a higher precision e.g. 32 will help. To understand why the overflow happened when you set the precision to 16, you can use NestList instead of Nest and remove ;{First[#], Rest[#]} &@Partition[yt, n] from the code and check the result, you'll see the Precision become lower and lower through the numeric calculation. BTW, you don't need Outer for JacobianMatrix, JacobianMatrix[funs_List, vars_List] := D[funs, {vars}] is enough. Apr16 reviewed Approve Is Sow/Reap compatible with Composition?