REVIEW ON THE USE OF CHEBYSHEV POLYNOMIALS FOR NUMERICAL MODELING OF APPLIED PROBLEMS

Chebyshev polynomials are widely used for numerical modeling of various applied problems. The main advantage of methods using Chebyshev polynomials is the high speed of convergence of calculation results. If - is the number of degrees of freedom (the number of Chebyshev polynomials or the number of nodes in a difference scheme), then when using difference methods the maximum error decreases as or (in difference methods of the second or fourth order of accuracy, respectively).