  A new formulation of the Maxwell equations based on two vector and two scalar
potentials is proposed. The use of these potentials allows the electromagnetic
field equations to be written in the form of a hyperbolic system. In contrast
to the original Maxwell equations, this system contains only evolutionary
equations and does not include equations having the character of differential
constraints. This fact makes the new equations especially convenient for
numerical simulations of electromagnetic processes; in particular, they can be
solved by modern powerful shock-capturing methods based on approximation of
spatial derivatives by upwind differences. The electromagnetic field both in
vacuum and in an inhomogeneous material medium is considered. Examples of
modeling the propagation of electromagnetic waves by means of solving the
formulated system of equations with the use of modern high-order schemes are
given.
  Key words: computational electrodynamics, two-potential formalism, numerical
solution of hyperbolic systems of equations, shock-capturing schemes.
