The talk is devoted to the results of the study of methods for numerical solution of a time-dependent Schrodinger equation. The fundamental possibility of the numerical solution of a time-dependent Schrodinger equation for a wave function defined on a non-uniform coordinate grid by the spectral method using the fast Fourier transform algorithm is discussed. The method is based on reducing the non-uniform coordinate grid to a uniform one by a non-linear transformation of coordinates and approximation of the obtained evolution operator using the Lee-Trotter-Suzuki product formula. Algorithms for the numerical solution of the first and second orders are constructed.