English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Recently, some authors have used the sinc-Gaussian sampling technique to approximate eigenvalues of boundary value problems rather than the classical sinc technique because the sinc-Gaussian technique has a convergence rate of the exponential order, O ( e − ( π − h σ ) N / 2 / N ) $O (e^{-(\pi-h\sigma)N/2}/\sqrt{N} )$ , where σ, h are positive numbers and N is the number of terms in sinc-Gaussian technique. As is well known, the other sampling techniques (classical sinc, generalized sinc, Hermite) have a convergence rate of a polynomial order. In this paper, we use the Hermite-Gauss operator, which is established by Asharabi and Prestin (Numer. Funct. Anal. Optim. 36:419-437, 2015), to construct a new sampling technique to approximate eigenvalues of regular Sturm-Liouville problems. This technique will be new and its accuracy is higher than the sinc-Gaussian because Hermite-Gauss has a convergence rate of order O ( e − ( 2 π − h σ ) N / 2 / N ) $O (e^{-(2\pi-h\sigma)N/2}/\sqrt {N} )$ . Numerical examples are given with comparisons with the best sampling technique up to now, i.e. sinc-Gaussian

A Hermite-Gauss method for the approximation of eigenvalues of regular Sturm-Liouville problems