Solve a PDE by using NDSolve?

Questions
,
1

I try to solve my equations by using NDsolve. But it does not solve my solution. Can anyone help me to check whether I used correct command or not?

eq1 = {D[Subscript[\[Theta], c][x, y], x] - 
     2/(Y - Y^2)*D[Subscript[\[Theta], c][x, y], y, y] == 0};
ic = {Subscript[\[Theta], c][0, y] == 1};
bc = {DirichletCondition[{Subscript[\[Theta], c][x, y] == 0}, y == 0],NeumannValue[0, y == 1]};

sol = NDSolve[{eq1, ic, bc}, {Subscript[\[Theta], c]}, {x, 0, 1}, {y, 
   0, 1}]
2

When I copy eq1 into Mathematica, I get a message

Syntax::bktmcp: Expression "{D[Subscript[\[Theta],c][x,y],x]-2/(Y-Y^2)*D[Subscript[\[Theta],c][x,y],y,y]==0" has no closing "}".
3

Thanks for your help. But I checked after correction it does not give me a result.

4

Mirza,

You had several bugs/typos:

  1. Y and y are different variables – be careful of capitalization
  2. you need a list of equations – not a list of lists
  3. you use NeumannValue incorrectly – it is not used in the boundary conditions it is in the equation itself (even though it acts at the boundary)
  4. you use extra lists in places they do not belong (i.e inside of DirichletCondition, the integration variable, etc.)

this computes a solution:

eq1 = {D[Subscript[\[Theta], c][x, y], x] - 
     2/(y - y^2)*D[Subscript[\[Theta], c][x, y], y, y] == 
    NeumannValue[0, y == 1]};
ic = {Subscript[\[Theta], c][0, y] == 1};
bc = {DirichletCondition[Subscript[\[Theta], c][x, y] == 0, y == 0]};

sol = NDSolve[Join[eq1, ic, bc], 
  Subscript[\[Theta], c], {x, 0, 1}, {y, 0, 1}]

Regards,

Neil

5

Thanks for your correction. But still, it does not give me the solution.