Solve the partial differential equation u$\_$t $=2$u$\_$xx $-$ u$\_$yy on the rectangular region $0<$ x $<\backslash$pi $,0<$ y $<\backslash$pi $/2,$ subject to the boundary conditions u$($x$,0)=$ u$($x$,\backslash$pi $/2)=$ u$(0,$ y$)=$ u$(\backslash$pi $,$ y$)=0$ and the initial condition u$($x$,$ y$,0)=$ f$($x$,$ y$)$