Solving of partial differential equations by schemes with complex coefficients

Complicated problems of high temperature gas dynamic flows with chemical reactions are described with a system of differential equations, as ordinary (ODE), so in partial derivatives. Traditional method of solving such problems is splitting on physical processes. Here is developed another way. All partial differential equations are transformed with the line method to a large stiff ODE system. This system is solved by explicit-implicit Rosenbrock scheme with complex coefficients, having some unique properties. The applications of this method are given for different types of problems, so as heat conduction, chemical reactions with heat conduction and diffusion, transfer equation, acoustics, gas dynamics, and gas dynamics with chemical reactions, diffusion and heat conduction.