Additive schemes for systems of time-dependent equations of mathematical physics

Additive difference schemes are derived via a representation of an operator of a time dependent problem as a sum of operators with a more simple structure. In doing so, transition to a new time level is performed as a solution of a sequence of more simple problems. Such schemes in various variants are employed for approximate solving complicated time-dependent problems for PDEs. In the present work construction of additive schemes is carried out for systems of parabolic and hyperbolic equations of second order. As examples there are considered dynamic problems of the elasticity theory for materials with variable properties, dynamics problems for an incompressible fluid with a variable viscosity, general 3D problems of magnetic field diffusion.