  Modification of coupled integral equations method (CIEM) for calculating the
characteristics of the accelerating structures is presented in this paper. In
earlier developed CIEM schemes the coupled integral equations are derived for
the unknown electrical fields at interfaces that divide the adjacent volumes.
In addition to the standard division of the structured waveguide by interfaces
between the adjacent cells, we propose to introduce new interfaces in places
where electric field has the simplest transverse structure. Moreover, the
system of coupled integral equations is formulated for longitudinal electrical
fields in contrast to the standard approach where the transverse electrical
fields are unknowns. The final matrix equations contain expansion coefficients
of the longitudinal electric field at these additional interfaces. This
modification makes it possible to deal with a physical quantity that plays an
important role in the acceleration of particles (a longitudinal electric
field), and to obtain approximate equations for the case of a slow change in
the waveguide parameters.
