Development of methods for solving the tasks of the continium linear programming using Legendre polynomials

Abstract

The article demonstrates the theoretical foundations of the mathematical apparatus − the continuum of linear programming. It demonstrates a technique for solving problems with the use of orthogonal systems of functions. The article was an exact solution of the problem of variational calculus to linear constraints. The purpose of the work is to develop accurate methods of solving the problem in the class of Legendre polynomials