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
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