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NDSolve[{(2 π ϵ Cos[2 π x] Sech[κ + ϵ κ Sin[2 π x]]^2 (2 κ + 2 ϵ κ Sin[2 π x] - 
         Sinh[2 κ (1 + ϵ Sin[2 π x])]))/(κ (1 + ϵ Sin[2 π x])^2) + 
         4 π ϵ Cos[2 π x] (1 + ϵ Sin[2 π x])^2 Derivative[1][p][x] + 
         2/3 (1 + ϵ Sin[2 π x])^3 (p'')[x] == 0, 
  p[0] == 0, p[1] == 0}, p, x, 
  Method -> {"Shooting", "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]

On running this code, the error getting displayed is

NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

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2
  • $\begingroup$ In the environment click on the triple dot symbol and click on the entry NDSolve::ndnum. There is instruction that will help You further. For me the instruction tells, give a value to the parameters with With! $\endgroup$
    – Steffen Jaeschke
    Commented Dec 30, 2023 at 15:10
  • $\begingroup$ @Trueee Parameter \[Epsilon],\[Kappa] are undefined. Check the form of the derivatives in your ode, should be p'[x],p''[x] $\endgroup$
    – Ulrich Neumann
    Commented Dec 30, 2023 at 17:23

1 Answer 1

Reset to default
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Try ParametricNDSolveValue (I corrected the derivatives ...)

P = ParametricNDSolveValue[
      {(2 π ϵ Cos[2 π x] Sech[κ + ϵ κ Sin[2 π x]]^2 (2 κ + 2 ϵ κ Sin[2 π x] - Sinh[2 κ (1 + ϵ Sin[2 π x])]))/(κ (1 + ϵ Sin[2 π x])^2) + 4 π ϵ Cos[2 π x] (1 + ϵ Sin[2 π x])^2  p'[x] + 2/3 (1 + ϵ Sin[2 π x])^3  p''[x] == 0,
       p[0] == 0, p[1] == 0},
      p,
      {x, 0, 1},
      {ϵ, κ}, Method -> {"Shooting", "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}
    ]

Plot[P[.5, 0.15][x], {x, 0, 1}]

enter image description here

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