On coincidence of the differential scheme of non-local border problem for pseudo-parabolic equation of the third order with variable factor

This work presents the a priori estimation in differential form for the solution of a non-local border problem for pseudo-parabolic equation of the third order. Hence the uniqueness and stability of the solution by initial data and the right part in the norm $W^1_2 (0, l)$ on the layer, and also the difference scheme of the second order of approxi-mation by the steps of the grid. The scheme is stable in it’s right part and initial data and coincides, moreover, the degree of the accuracy coincides with the degree of approximation. Numeric experiments are performed.