In the presented work, a discrete analog of the Fourier method is applied to the solution of a mixed problem with non-classical boundary conditions. Non-local problems for differential equations are called problems in which, instead of the usual boundary conditions, conditions are specified that connect the values of the solution or its derivatives at various points of certain boundary manifolds or at points of the boundary and at points of some internal manifolds. Various applied problems of mechanics and physics are brought to non-local boundary value problems for partial differential equations. The used discrete Fourier analog allows us to estimate the error of the method only through the known data of the problem. The corresponding finite difference scheme is constructed and the error of the approximate solution is estimated. This assessment involves only known data for the task at hand, and this makes it possible to effectively estimate the error of the method.