Prescribing strange boundary conditions

Question

Does anyone know how to prescribe boundary conditions of like u[t,0,y]==u[t,1,1-y] in Mathematica using NDSolve... It always complains that the arguments of the dependent variable should literally match the independent variable.

Thanks in advance.

Answer 1

This symmetry condition can probably be recast in the form Derivative[0,1][u][x,1/2]==0. Of course, more information on the problem would be helpful.

Edit in response to rcollyer: The algebraic identity f(x)=f(1-x) for all x in (0,1) implies a geometric symmetry: the graph of f will be symmetric about the line x=1/2. Now draw the graph of such a function; if it is differentiable, you will find that f'(1/2)=0.

Now, I don't know for sure that the OP's problem can be recast this way; it rather depends on the specifics of the problem. This situation frequently arises when dealing with PDEs on the disk where the function u is a function of polar coordinates r and theta. If the disk represents a clamped drum, then perhaps you've got u(1,t)=0. But, what of u(0,t)? If the function is symmetric and smooth, then u_x(0,t)=0 is a reasonable condition.