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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

- We consider the difference scheme of the solution to the Dirichlet problem for the Laplace equation in a cylinder, using the linear Collatz interpolation at near-boundary mesh nodes. The upper uniform bound of the error of the form O (h 2  In h -1 ) obtained by the author in [10] for both the lateral surface of a cylinder and its boundary values of class C 1,1  is proved to be unimprovable in order with respect to the grid step h. It is also established that an additional requirement of the existence of the continuous second derivatives in boundary values on the lateral surface of the cylinder does not ensure the convergence of the difference solution with rate h even if the cylinder is circular. We derive the upper uniform bound of the error of order h for the sufficiently smooth lateral surface of the cylinder and the boundary values of class C 2,λ ,0 &lt; λ &lt; 1. These boundary values are supposed to satisfy a compatibility condition on the edges of the cylinder, which results from the Laplace equation.

On upper and lower bounds of the error of the difference solution to the Dirichlet problem for the Laplace equation in a cylinder