On strong solutions of a $B$-elliptic boundary-value problem and its difference approximation

In this work, a finite-difference scheme for a boundary-value problem for a $B$-elliptic equation is constructed. The convergence is examined in the Kipriyanov weight space. An integral balance relation for the exact solution of the original problem is obtained by using Steklov averaging operators. A five-point difference scheme and an a priori estimate for the error are obtained.