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/

Zendy Plus

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

Zendy Tools

Zendy Open

We propose the generalized quadrature methods for numerical solution ofsingular integral equation of Abel type. We overcome the singularity using theanalytical calculation of the singular integral expression. The problem ofsolution of singular integral equation is reduced to nonsingular system oflinear algebraic equations without shift meshes techniques employment. We alsopropose generalized quadrature method for solution of Abel equation using thesingular integral. Relaxed errors bounds are derived. In order to improve theaccuracy we use Tikhonov regularization method. We demonstrate the efficiencyof proposed techniques on infrared tomography problem. Numerical experimentsshow that it make sense to apply regularization in case of highly noisy sourcesonly. That is due to the fact that singular integral equations enjoyselfregularization property.

Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography