Version 1
: Received: 30 September 2024 / Approved: 30 September 2024 / Online: 30 September 2024 (17:44:26 CEST)
How to cite:
Poghosyan, A.; Poghosyan, L.; Barkhudaryan, R. On a Convergence of Quasi-Periodic Interpolations Exact for the Polyharmonic-Neumann Eigenfunctions. Preprints2024, 2024092463. https://doi.org/10.20944/preprints202409.2463.v1
Poghosyan, A.; Poghosyan, L.; Barkhudaryan, R. On a Convergence of Quasi-Periodic Interpolations Exact for the Polyharmonic-Neumann Eigenfunctions. Preprints 2024, 2024092463. https://doi.org/10.20944/preprints202409.2463.v1
Poghosyan, A.; Poghosyan, L.; Barkhudaryan, R. On a Convergence of Quasi-Periodic Interpolations Exact for the Polyharmonic-Neumann Eigenfunctions. Preprints2024, 2024092463. https://doi.org/10.20944/preprints202409.2463.v1
APA Style
Poghosyan, A., Poghosyan, L., & Barkhudaryan, R. (2024). On a Convergence of Quasi-Periodic Interpolations Exact for the Polyharmonic-Neumann Eigenfunctions. Preprints. https://doi.org/10.20944/preprints202409.2463.v1
Chicago/Turabian Style
Poghosyan, A., Lusine Poghosyan and Rafayel Barkhudaryan. 2024 "On a Convergence of Quasi-Periodic Interpolations Exact for the Polyharmonic-Neumann Eigenfunctions" Preprints. https://doi.org/10.20944/preprints202409.2463.v1
Abstract
Fourier expansions by the polyharmonic-Neumann eigenfunctions showed improved convergence compared to the Fourier expansions by the classical trigonometric system due to the rapid decay of the corresponding Fourier coefficients. Based on this evidence, we investigate interpolations on a finite interval that are exact for the polyharmonic-Neumann eigenfunctions and show the same benefits. Further, we improve the convergence of the interpolations by applying the idea of quasi-periodicity, where the basis functions are periodic on a slightly extended interval. We show that those interpolations have much better convergence rates away from the endpoints of the approximation interval. Moreover, the interpolations are more accurate on the entire interval. We prove those properties for a specific case of the polyharmonic-Neumann eigenfunctions known as the modified Fourier system. For other basis functions, we provide evidence based on the results of numerical experiments.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
