Stability of FDTD in curvilinear coordinates

A new approach suitable for determination of the maximal stable time step for the finite-difference time domain (FDTD) algorithm in curvilinear coordinates is presented. It is based on a modified variable separation method, applied to the set of difference equations of the FDTD algorithm. Investigation is carried out in spherical and cylindrical coordinates. A simple yet accurate enough approximative formula for cylindrical coordinates is presented. Applied to Cartesian coordinates, this approach yields the well-known Courrant condition.