Research of one interpolation formula at creation of the finite-difference scheme for functions with internal zones of the bigger gradients

Abstract In work the method creation of the interpolation formula which is bringing closer function of the smoothing gap, meeting in solutions of one-dimensional tasks with a heatmass transfer is investigated. Interpolation on the basis of the decision for the smoothing gap is used for creation of finite-difference schemes to multidimensional tasks with ruptures of the first sort in boundary and initial and regional conditions. Use of additional knots with the constructed interpolation gives considerable reduction of approximating viscosity in finite-difference schemes for the convective and diffusive equations of transfer. For the constructed interpolation in case of existence of an internal interface which thickness less step of a regular grid is conducted an accuracy research at the asymptotic approximations in small parameters corresponding to changes of required function in the neighborhood of a thin interface. The carried-out numerical calculations on a heat and mass transfer for a test task in two-dimensional rectangular area on the basis of the developed method show increase in an asymptotic order of accuracy of numerical decisions to the second from a grid step at application of the known schemes in the wide range of small parameter of diffusion.