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.
Stacionarusis uždavinys su nelokaliomis kraštinėmis sąlygomis
Santrauka. Straipsnyje nagrinėjamas uždavinys su nelokoliosiomis kraštinėmis sąlygomis, susiejančiomis sprendinio reikšmę srities kraštuose su sprendinio reikšme vidiniame taške ir/arba sprendinio integralu. Tiriamas diferencialinis uždavinys ir baigtinių skirtumų schema, aproksimuojanti šį uždavinį. Gautos pakankamos sąlygos sprendinio egzistavimui ir vienačiai. Surastos sąlygos, kada sprendinys yra neneigiamas ir stabilus tolygioje normoje. Visi teoriniai rezultatai iliustruojami atitinkamais pavyzdžiais.
Čiegis, R., Štikonas, A., Štikoniene, O., & Suboč, O. (2001). Stationary problems with nonlocal boundary conditions. Mathematical Modelling and Analysis, 6(2), 178-191. https://doi.org/10.3846/13926292.2001.9637157
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
