ИСТИНА

We propose some new efficient approaches for asymptotic-numerical investigation of moving fronts in reaction-diffusion-advection models. On the example of numerical solution of the Burgers's equation with a small parameter at higher derivative we discuss some methods of dynamic adaptive meshes construction. For corresponding construction we use a priori information based on asymptotic analysis of the problem. In particular, we take into account some information about the speed of the transition layer, its width and structure. Our algorithms are able to significantly reduce the complexity of the numerical calculations in comparison with classical approaches for solving of this class problems.