Electromagnetic pulse scattered by a sphere

The magnetic field integral equation for transient electromagnetic scattering by a perfectly conducting sphere is solved by the stepping-in-time procedure. The contributions to the surface current density (SCD) from the self-patch, where the integrand is singular, and from the neighboring patches can be computed by formulas that are more accurate for these patches than the simple product used for other patches. These formulas have to include the time-derivative term of the integrand for the computation of the initial (small) values of the SCD. The improvement in the values of the scattered fields due to these corrections is significant but not dramatic.