Stability analysis of the Peaceman-Rachford method for parabolic equations with nonlocal conditions
Date
2022-06-30
Authors
Sapagovas, Mifodijus
Novickij, Jurij
Ciupaila, Regimantas
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Nonlocal boundary conditions, Parabolic equations, Alternating direction method, Stability of finite difference scheme
Citation
Sapagovas, 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.
Rights
Attribution 4.0 International