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Get solution of a PDE with NDSolve?

Posted 4 years ago

This example of PDE I found in a textbook and would like to know is there any way to solve it using DirichletCondition or NeumannValue or some other way.

eq = {50*Derivative[2, 0][T][x, t] == 2423750*Derivative[0, 1][T][x, t]};
inc = {Derivative[1, 0][T][0, t] == 0, Derivative[1, 0][T][1, t] == 5863/10 - 2*T[1, t], T[x, 0] == 9463/20}; 
NDSolve[Join[eq, inc], T, {x, 0, 1}, {t, 0, 20}] // Flatten
NDSolve::ibcinc: Warning: boundary and initial conditions are inconsistent.

I am grateful for any tips. Sinval

POSTED BY: Sinval Santos
2 Replies
Posted 4 years ago

Thank you for the tips.

POSTED BY: Sinval Santos

In this problem, it is necessary to coordinate the initial and boundary conditions, as well as use the solution method and increase the time interval to 200 for clarity.

eq = { 2423750 Derivative[0, 1][T][x, t] - 
     50  Derivative[2, 0][T][x, t] == 0};
bc = {Derivative[1, 0][T][0, t] == 0, 
   Derivative[1, 0][T][1, 
     t] == (5863/10 - 2*T[1, t]) (1 - Exp[-10 t])};
ic = T[x, 0] == 9463/20;
sol = NDSolveValue[{eq, ic, bc}, T, {x, 0, 1}, {t, 0, 200}, 
  Method -> {"MethodOfLines", 
    "SpatialDiscretization" -> {"TensorProductGrid", 
      "MinPoints" -> 40, "MaxPoints" -> 100, 
      "DifferenceOrder" -> "Pseudospectral"}}, MaxSteps -> 10^6]


{Plot3D[Re[sol[x, t]], {x, 0., 1}, {t, 0, 200}, Mesh -> None, 
  ColorFunction -> Hue, PlotRange -> {450, 500}, 
  AxesLabel -> Automatic], 
 Plot3D[Re[sol[x, t]], {x, 0.9, 1}, {t, 0, 200}, Mesh -> None, 
  ColorFunction -> Hue, PlotRange -> {450, 500}, 
  AxesLabel -> Automatic]}

Figure 1

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