METHODS FOR EVALUATING THE CONVERGENCE RATE AND ACCURACY OF SPECTRAL METHODS

This article provides a comprehensive analysis of methods for evaluating the convergence rate and accuracy of spectral methods. The study examines error norms, the decay rate of spectral coefficients, and discretization errors based on Fourier and Chebyshev spectral methods. In addition, the influence of function smoothness and boundary conditions on convergence is discussed. The obtained results demonstrate the advantages of spectral methods in high-precision numerical modeling and substantiate their effective application in practical problems.