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TWO questions to experts ...

Hi all,
My questions are following:

1)IS THERE A GOOD PROGRAMME WHICH CAN SOLVE (numerically) THE SCHRODINGER
  EQUATION WITH (ARBITRARY) BOUNDARY-INITIAL CONDITIONS?

2)Does exist a program which can solve (numerically) a large class
  of partial differential equations 2-nd orders (ellitic, parabolic,
  hyperbolic) with arbitrary boundary conditions?

BTW. 
  How could do this program when a equation with fixed boundary conditions
  has no solution?