Features of calculating contrast structures in the Cauchy problem

Abstract

In solving stiff Cauchy problems, regions of a very rapid change in the solution, which are called boundary layers, arise. In nonlinear problems, there may be several such regions and not only at the initial moment but at different times when they are called contrast structures. It is shown that in the numerical solution of contrast structures, round-off errors can become so great that even a significant increase in the digit capacity is unable to resolve the situation. In this case, approximate analytical methods developed in boundary layer theory turn out to be more effective. As an applied problem, we consider a numerical solution of a real problem of chemical kinetics, i.e., combustion of hydrogen in oxygen. It is shown that this process involves the emergence of a contrasting structure due to the production of transitional chemical components. Therefore, the actual flare of the flame occurs not at the initial moment but after a delay.