Decomposition implementation of Horner's scheme for calculating the values of multidimentional polynomials

The paper presents a decomposition implementation of Horner's scheme for calculating the values of multidimensional polynomials, which reduces the problem to calculating a sequence of values of one-dimensional polynomials according to Horner's scheme. The possibility of using this scheme in a distributed computer environment is studied. The operation of the scheme is exemplified by the problem of constructing approximate analytical solutions of differential equations with a polynomial right-hand side.