Skip to main content

parametricNDSolve for solving differential equation


i want to solve this equation and plot it solution w.r.t N2 and theta(0)


theta''[x] + 2*theta'[x] - Exp[-2*x]*(N2)^2*(theta[x] - 5) + Q1 == 0 anyone please help



Answer



It is not clear what you want plotted nor how you want the plots done. Neither have you specified the range of the variables that are of interest. The following will need to be tailored once you understand your needs.



Clear["Global`*"]

{xmin, xmax} = {0, 1};

Manipulate[
 Module[{eqns1, sol1},
  eqns1 = 
  {theta''[x] + 2*theta'[x] - Exp[-2*x]*N21^2*(theta[x] - 5) + Q11 == 0, 
    theta[0] == t01, theta'[0] == tp01};
  sol1 = ParametricNDSolve[eqns1, theta, {x, xmin, xmax}, N21];

  Plot3D[Evaluate[theta[N21][x] /. sol1],
   {x, xmin, xmax}, {N21, 0, 5},
   AxesLabel -> (Style[#, 14, Bold] & /@ {"x", "N2", "theta"}),
   ClippingStyle -> None]],
 {{Q11, 5, Q1}, 0, 10, Appearance -> "Labeled"},
 {{t01, 0, "theta[0]"}, 0, 10, Appearance -> "Labeled"},
 {{tp01, 0, "theta'[0]"}, 0, 10, Appearance -> "Labeled"}]
(* spacer *)

enter image description here



Manipulate[
 Module[{eqns2, sol2},
  eqns2 = 
  {theta''[x] + 2*theta'[x] - Exp[-2*x]*N22^2*(theta[x] - 5) + Q12 == 0, 
  theta[0] == t02, theta'[0] == tp02};
  sol2 = ParametricNDSolve[eqns2, theta, {x, xmin, xmax}, t02];
  Plot3D[Evaluate[theta[t02][x] /. sol2],
   {x, xmin, xmax}, {t02, 0, 5},
   AxesLabel -> (Style[#, 14, Bold] & /@ {"x", "theta[0]", "theta"}),
   ClippingStyle -> None]],

 {{Q12, 5, Q1}, 0, 10, Appearance -> "Labeled"},
 {{N22, 5, N2}, 0, 10, Appearance -> "Labeled"},
 {{tp02, 0, "theta'[0]"}, 0, 10, Appearance -> "Labeled"}]
(* spacer *)

enter image description here


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

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more