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 3h comment Numerical solution of IVP for linear ODE with variable coefficient runs wild soon You may want to take part in the discussion here, currently the transformation can be done by Assuming[0 < t < Pi/2, dChange[eqn, ArcTan@x == t, x, t, y[x]]]. :D 3h comment Numerical solution of IVP for linear ODE with variable coefficient runs wild soon The "DifferenceOrder" seems not to be helpful here, at least when it's together with "ImplicitRungeKutta" or "ExplicitRungeKutta"… 8h comment Subsituting expressions for expressions @F.E. I don't think there's any serious downside, it's just OK to use a[c] and b[d] directly. Of course it's better to use With when there's a lot of a[c]/b[d] to write. 2d comment In WolframAlpha, how can I make a Scatter Plot without connecting points? Seems that parentheses aren't necessary: wolframalpha.com/input/… Apr23 comment Better method to swap the values of two 2-D arrays There are two $a_{k+1,k+1}$ in the matrix? Apr23 comment Solving coupled differential equations with an eigenvalue I noticed that you've modified your equations for several times, are you sure it's correct this time? Maybe you can show us the original problem? Apr23 comment Bizarre Compile Error, changing one symbol Where's the definition of nSites? 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 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 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 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 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. Apr15 comment 3D scatter plot with labels Show[Graphics3D[{Blue, PointSize[0.02], Point[data]}], Graphics3D[ Text[#[[1, 1]], 1.04*#[[2]]] & /@ Transpose@{labels, data}], Axes -> True, BoxRatios -> 1] Apr14 comment Trying to model Heat flow trough different materials with NDsolve BTW, let alone the vagueness of this question, how to Implement heat flux continuity condition is indeed a interesting question, I do find a solution for this, but not that general and I'm not satisfied. I'm hesitating whether I should post it as an answer or start a new question, which will of course state the problem in a clearer way. Apr14 comment Trying to model Heat flow trough different materials with NDsolve Just a sidenote, I believe that OP and @Laurent and this OP did want to add a flux continuity condition, they just didn't understand what a flux continuity condition is very well. Flux continuity condition depends on heat conductivity coefficient (usually notated with $\lambda$) rather than thermal diffusivity (usually notated with $\alpha$, for OP's question, (1 + 4 UnitStep[5 - x])/5. plays the role of thermal diffusivity exactly. ) Apr13 comment Assumptions with patterns @Fabio Well, the above code has been tested in v9.0.1, vista 32bit. Have you tried it with a fresh kernel?