Numerical Solution and High-Order Error Determination for the Problems with Non-Classical Boundary Condition

A problem with a non-classical boundary condition is considered. By means of the discrete analog of Fourier method in case with the non-local Dirichlet problem for Laplace equation difference scheme of fourth order of approximation is constructed. The efficient error estimate of the order (h
⁴
) is obtained, that is, only known task data are involved in this evaluation.