Skip to main content

plotting - Exporting the solutions of two ODEs sampled over same set of domain values



I have two functions h[r] and c[r] defined by two differentials equation.


operh[h_, c_] := h D[D[h, r, r] + 1/r D[h, r] - 1/lc^2 h, r] + m D[c, r]
operc[h_, c_] := 
  cmt h + ξ ((ϕ - H) (1 - ϕ) )/Sqrt[R^2 - r^2] - 
    1/r D[r h (1 + e^2/1680  h^4  (D[c, r])^2 ) D[c, r], r]

I numerically solve them with NDSolve (with solution called "s" here under). Then I plot them with no problem:



Plot[h[r] /. s, {r, rleft, rright}, PlotRange -> All, AxesOrigin -> {0, 0}]
Plot[c[r] /. s, {r, rleft, rright}, PlotRange -> All, AxesOrigin -> {0, 0}]

With same rright and rleft.


graph for h graph for c


What I want is a .txt or .csv file with 3 columns, containing r, h[r] and c[r]. From what I have read on this site I tried:


ploth = 
  Plot[h[r] /. s, {r, rleft, rright}, PlotRange -> All, AxesOrigin -> {0, 0}]
pts = Cases[ploth, Line[pts_] :> pts, Infinity][[1]]
Export[SystemDialogInput["FileSave", "filename.csv"], pts]


It gave me a list of 157 pairs {r, h[r]}. Then I did the same for c:


plotc = 
  Plot[c[r] /. s, {r, rleft, rright}, PlotRange -> All, AxesOrigin -> {0, 0}]
pts = Cases[plotc, Line[pts_] :> pts, Infinity][[1]]
Export[SystemDialogInput["FileSave", "filename.csv"], pts]

And it gave me a list of 226 pairs {r, c[r]}. This is not the same number of data than for h(r), so I can't merge them.


I tried by plotting the two curves on a single graph but it gave me only one of the two data sets.


I also tried to use Table but it gave me an empty list:



tableh = Table[{r, ploth}, {r, rleft, rright}]


{}



Do you know how to extract h and c data for common r values?


I'm on Mathematica 7.0



Answer



An approach to this issue I like is to rely on the fact that NDSolve found the solution on the same grid points for both functions in the first place:


a simple example:



 sol = First@NDSolve[ {f''[x] + g'[x] + 1 == 0 , g[x] == x^2, f[0] == 0, 
   f'[0] == 1}, {f, g}, {x, 0, 1}];
 Plot[{f[x] /. sol, (g[x] /. sol)}, {x, 0, 1}]

enter image description here


here we do not actually use the interpolation but extract the grid values:


 gridpoints = Flatten[(g /. sol)["Grid"]];
 computeddata = 
    Transpose[{gridpoints, 
              (f /. sol)["ValuesOnGrid"],

              (g /. sol)["ValuesOnGrid"]}];
 ListPlot[{ computeddata[[All, {1, 2}]], computeddata[[All, {1, 3}]]}, 
  Joined -> True, PlotMarkers -> Automatic]

enter image description here


here computeddata is a nice array you can simply export with each row {x,f[x],g[x]}


An advantage to this is the point spacing is naturally refined as was needed by NDSolve


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

plotting - Magnifying Glass on a Plot

Although there is a trick in TEX magnifying glass but I want to know is there any function to magnifying glass on a plot with Mathematica ? For example for a function as Sin[x] and at x=Pi/6 Below, this is just a picture desired from the cited site. the image got huge unfortunately I don't know how can I change the size of an image here! Answer Insetting a magnified part of the original Plot A) by adding a new Plot of the specified range xPos = Pi/6; range = 0.2; f = Sin; xyMinMax = {{xPos - range, xPos + range}, {f[xPos] - range*GoldenRatio^-1, f[xPos] + range*GoldenRatio^-1}}; Plot[f[x], {x, 0, 5}, Epilog -> {Transparent, EdgeForm[Thick], Rectangle[Sequence @@ Transpose[xyMinMax]], Inset[Plot[f[x], {x, xPos - range, xPos + range}, Frame -> True, Axes -> False, PlotRange -> xyMinMax, ImageSize -> 270], {4., 0.5}]}, ImageSize -> 700] B) by adding a new Plot within a Circle mf = RegionMember[Disk[{xPos, f[xPos]}, {range, range/GoldenRatio}]] Show...
Post a Comment
Read more