Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 44, pp. 1-15.

Title: Stability analysis of the Peaceman-Rachford method for parabolic equations with nonlocal conditions
       
Authors: Mifodijus Sapagovas (Vilnius Univ., Vilnius, Lithuania)
         Jurij Novickij (Vilnius Univ., Vilnius, Lithuania)
         Regimantas Ciupaila (Vilnius Gediminas Technical Univ., Vilnius, Lithuania)

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.     

Submitted October 9, 2021. Published June 30, 2022.
Math Subject Classifications: 65M06, 35K20, 34B10, 34K20.
Key Words: Nonlocal boundary conditions; parabolic equations; 
          alternating direction method; stability of finite difference scheme.