Locally One-Dimensional Difference Scheme for a Nonlocal Boundary Value Problem for a Parabolic Equation in a Multidimensional Domain.

We study a nonlocal boundary value problem for a parabolic equation in the multidimensional case. A locally one-dimensional difference scheme is constructed to solve this problem numerically. A priori estimates are derived by the method of energy inequalities in the differential and difference settings. The uniform convergence of the locally one-dimensional scheme is proved. [ABSTRACT FROM AUTHOR]