  An efficient scheme for one-dimensional extensive air shower simulation and
its implementation in the program CONEX are presented. Explicit Monte Carlo
simulation of the high-energy part of hadronic and electromagnetic cascades in
the atmosphere is combined with a numeric solution of cascade equations for
smaller energy sub-showers to obtain accurate shower predictions. The developed
scheme allows us to calculate not only observables related to the number of
particles (shower size) but also ionization energy deposit profiles which are
needed for the interpretation of data of experiments employing the fluorescence
light technique. We discuss in detail the basic algorithms developed and
illustrate the power of the method. It is shown that Monte Carlo, numerical,
and hybrid air shower calculations give consistent results which agree very
well with those obtained within the CORSIKA program.
