(untitled) (Journal of the College of Basic Education, 2023)
In this paper, the generalized Chebyshev polynomials defined on the interval [a,b] are presented. Some properties of such polynomials that are useful for numerical applications are discussed and derived. Then a direct method for solving variational problems is proposed which is based on the generalized Chebyshev polynomials to reduce a variational problem to a nonlinear mathematical programming problem. The solution is obtained in terms of generalized Chebyshev polynomials method, illustrative examples is given.