Find the solution of the Neumann problem for the LaPlace equation

\bigtriangledown ^2U(x,y)=0; U_{x}(0,y)=cos(4 \pi x)=U_x(4,y)=U_y(x,0)=U_y(x,4)

On the square region

R={(x,y):x\varepsilon [0,4], y\varepsilon [0,4]}