A Note on Stability of Parabolic Difference Equations on Torus

The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.