Abstract. An explicit multistep one-stage method is considered, which allows numerical integration of the differential equations that constitute the basis of the atmosphere circulation model, by transforming the initial–boundary-value problem of convective diffusion to the Cauchy problem The method has an advantage over the existing methods due to its high precision and low computational cost.

Keywords: convection–diffusion problem, discrete representation of partial derivatives, Cauchy problem for ODE, multistep method.