Numerical method for solving a nonlocal boundary value problem for a multidimensional parabolic equation

The work is devoted to nonlocal boundary value problems for a multidimensional parabolic equation with variable coefficients. The method of energy inequalities is used to obtain a priori estimates in differential and difference interpretations for solutions of nonlocal boundary value problems. The obtained estimates imply the uniqueness and stability of the solution of each of the considered problems with respect to the right-hand side and initial data, as well as the convergence of the solution of the difference problem to the solution of the original differential problem in the $L_2$-norm at a rate of $O(|h|+\tau)$. For each of the considered problems, a numerical solution algorithm is constructed, and numerical calculations of test examples are carried out.