The use of orthogonal polynomials in the differential transformations

In electrical engineering, automation, mechanics and other fields the integration transformations have been widely spread. The initial differential equations are transformed to the more simply algebraic equations by this transformation. However, application of these operators does not give the analysis of systems with variable and nonlinear parameters, especially at study of nonstationary processes, appreciable advantages on comparison with the known numerical methods. For the problem solution it is possible to take an advantage of conversion to basis of first kind of orthogonal Chebyshev polynomials, and also to basis of biased Chebyshev polynomials