QS1 POLYNOMIALS

Abstract

The author earlier developed new classes of quasi-spectral polynomials, and the study presents new findings about these classes for the efficient resolution of mathematical physics problems. By examining the approximation behavior of Fourier series by systems of quasispectral polynomials and the accompanying order of approximation, we explore the potential for retrieving information about functions that are solutions of boundary value problems. This work proves that the function, which in practice is the Sobolev space solution of the boundary value problem, can be reconstructed with the same accuracy in the base space of all square summable functions as it could be reconstructed if it were explicitly given.