LQ-DECREASING MONOTONIC SCHEMES WITH COMPLEX COEFFICIENTS AND APPLICATIONS TO COMPLICATED PDE SYSTEMS

Many important applied problems, for example high temperature gas dynamic flows in chemical reactions, are described by a complicated system of partial differential equations (PDEs) which may be reduced to large systems of ordinary differential equations (ODEs) that are usually stiff. Some essential qualitative requirements have been proposed for numerical methods that are designed for stiff problems. In some cases schemes with complex coefficients appeared to be the best from this point of view. They are simple and explicit and numerical examples show they are very reliable, have good consistency and may be recommended for a wide range of problems.