Stationary problems with nonlocal boundary conditions

Abstract

In this article a stationary problems with general nonlocal boundary conditions is considered. The differential problems and finite difference schemes for solving this problem are investigated. Stability estimates are proved in the maximum norm and the non‐negativity of the solution is investigated. All theoretical results are illustrated by representative examples.

Straipsnyje nagrinejamas uždavinys su nelokoliosiomis kraštinemis salygomis, susiejančiomis sprendinio reikšme srities kraštuose su sprendinio reikšme vidiniame taške ir/arba sprendinio integralu. Tiriamas diferencialinis uždavinys ir baigtiniu skirtumu schema, aproksimuo‐janti šj uždavini. Gautos pakankamos salygos sprendinio egzistavimui ir vienačiai. Surastos salygos, kada sprendinys yra neneigiamas ir stabilus tolygioje normoje. Visi teoriniai rezultatai iliustruojami atitinkamais pavyzdžiais.