Variational approach and Euler's integrating factors for environmental studies

One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection-diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids.