Solving differential equations with xCoba expressions

[Lukas Wutschitz]

I have to solve a differential equation in a curvilinear frame and xCoba worked great to get the equation into the correct form. But now when I'm trying to solve it I'm a bit stuck. I'm used to use DSolve in this case and it has worked great for simple equations like Laplace's equation:

DSolve[{

  D[f[x, y], {x, 2}] + D[f[x, y], {y, 2}] == 0,(* Laplace equation *)

    f[0, y] == y,(* Boundary conditions *)

  f[1, y] == y,

  f[x, 0] == 0,

  f[x, 1] == 1

  }, f, {x, y}](* Solve for f[x,y] *)

However, when I use DSolve for expression I obtained from xAct manipulations it doesn't seem to recognise the differential operators. I've been looking for a while now for solutions but nothing seems to work.

[magma]

Can you post the explicit  xAct expression that you wish to solve?

Alessandro

[Lukas Wutschitz]

Hi,

Thanks for the quick reply. I first tried to solve a reduced problem:

I define the environment 

DefManifold[M, 2, IndexRange[a, f]]
DefChart[B, M, {1, 2}, {x[], y[]}]
DefParameter[t]
DefTensor[u[], {M, t}]

And I would like to solve a simple equation like this

ParamD[t][u[]] == 1
PD[-a][u[]] == 0

The output generated by xAct makes me think I'm on the right track. Or at least, I would write the PDE exactly like this with pen and paper. But obviously DSolve doesn't know what to do with it. Because t and other symbols are defined to be xAct objects.

DSolve[{
  ParamD[t][u[]] == 1,
  PD[-a][u[]] == 0
  },
 u[], t]

Thank you for your help.