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« **on:** October 10, 2012, 11:07:51 PM »
Here is my solution to this problem

I used the same approach as Zarak did, but in part (d) I think we would have to consider Dirichlet and Neumann boundary conditions separately. For Dirichlet, u(t,0)=> V(t,0) and we can use method of continuation to solve the V(x,t) first and then get u(x,t).

But for Neumann boundary condition, ux(t,0)=0 => nV(t,0) + Vx(t,0)=0 which does not necessarily mean that V(t,0)=0 or Vx(t,0)=0. In this case the boundary conditions are not automatically satisfied and we might not be able to use method of continuation.

Please let me know if there's anything wrong with this solution. Thanks in advance!