  We present a general formalism allowing for efficient numerical calculation
of the production of massless scalar particles from vacuum in a one-dimensional
dynamical cavity, i.e. the dynamical Casimir effect. By introducing a
particular parametrization for the time evolution of the field modes inside the
cavity we derive a coupled system of first-order linear differential equations.
The solutions to this system determine the number of created particles and can
be found by means of numerical methods for arbitrary motions of the walls of
the cavity. To demonstrate the method which accounts for the intermode coupling
we investigate the creation of massless scalar particles in a one-dimensional
vibrating cavity by means of three particular cavity motions. We compare the
numerical results with analytical predictions as well as a different numerical
approach.
