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Get solution of a PDE with NDSolve?

Sinval Santos

Posted 6 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 = {50Derivative[2, 0][T][x, t] == 2423750Derivative[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

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

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Sinval Santos

Posted 6 years ago

Thank you for the tips.

POSTED BY: Sinval Santos

Alexander Trounev

Alexander Trounev, A&E Trounev IT Consulting

Posted 6 years ago

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]}

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]}

POSTED BY: Alexander Trounev

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