Numerical Solution of Time-Dependent Problems with Different Time Scales

Problems for time-dependent equations in which processes are characterized by different time scales are studied. Parts of the equations describing fast and slow processes are distinguished. The basic features of such problems related to their approximation are taken into account using finer time grids for fast processes. The construction and analysis of inhomogeneous time approximations is based on the theory of additive operator-difference schemes (splitting schemes). To solve time-dependent problems with different time scales, componentwise splitting schemes and vector additive schemes are used. The capabilities of the proposed schemes are illustrated by numerical examples for the time-dependent convection-diffusion problem. If convection is dominant, the convective transfer is computed on a finer time grid.