Sapagovas, MifodijusNovickij, JurijCiupaila, Regimantas2023-04-182023-04-182022-06-30Sapagovas, M., Novickij, J., & Ciupaila, R. (2022). Stability analysis of the Peaceman-Rachford method for parabolic equations with nonlocal conditions. <i>Electronic Journal of Differential Equations, 2022</i>(44), pp. 1-15.1072-6691https://hdl.handle.net/10877/16603We consider an efficient finite difference method solving of two-dimensional parabolic equations with nonlocal conditions. The specific feature of the investigated problem is that the nonlocal condition contains the values of solution's derivatives at different points. We prove the stability of this method in specific energy norm. The main stability condition is that all eigenvalues of the corresponding difference problem are positive. Results of computational experiments are presented.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalNonlocal boundary conditionsParabolic equationsAlternating direction methodStability of finite difference schemeArticle