A Note on Parabolic Difference Equations on Manifold

In this work, we consider nonlocal boundary value problems for parabolic equations on manifold. We set up the first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle. For the solutions of the difference scheme, we establish the stability estimates and coercivity estimates in various Hölder norms for the solutions of such boundary value problems. Furthermore, numerical results are given. © 2022 American Institute of Physics Inc.. All rights reserved.