Abstract
this article discusses the distribution of emissions of pollutants from traffic congestion at the intersections in Almaty city transport network. A mathematical model has been developed by using a recurrent operator method for modeling and calculating the spread of harmful impurities in the urban environment. To solve partial differential equations of the second order, integral-differential operators are introduced in the form of a special series with constant coefficients determined from the recurrence relations associated with the differential equation in question. The particular solutions obtained in this case are relatively simpler, since they were based on a single recurrence relation, which leads to simpler differentiation formulas. Based on the approach, the general solutions were proposed in terms of arbitrary functions and are not related to the solution with the definition of the roots of the characteristic equation of the function. The obtained results were illustrated graphically and given in tables.