Prikazchikov V.G., Khimich A.N.
Asymptotic estimates of the accuracy of eigenvalues of fourth order operator with mixed boundary conditions

We obtain the asymptotic estimates of the accuracy of eigenvalues of the fourth-order operator with mixed boundary conditions on the boundary of a rectangle. Knowledge of the main part of eigenvalues error allows us to reasonably specify eigenvalues on a sequence of grids, obtain discrete analogs of high accuracy, and construct discrete analogs whose eigenvalues give the bilateral approximation to eigenvalues of the original problem. © 2017, Springer Science+Business Media New York.

Keywords: accuracy estimate, difference scheme, elliptic operator, mixed boundary conditions, the principal term of error, Boundary conditions, accuracy estimate, Asymptotic estimates, Bilateral approximations, Difference schemes, Elliptic operator, Fourth order, High-accuracy, Mixed boundary condition, Eigenvalues and eigenfunctions

Cite:
Prikazchikov V.G., Khimich A.N. (2017). Asymptotic estimates of the accuracy of eigenvalues of fourth order operator with mixed boundary conditions. Cybernetics and Systems Analysis, 53 (3), 32-40. doi: https://doi.org/10.1007/s10559-017-9935-5 http://jnas.nbuv.gov.ua/article/UJRN-0000700156 [In Russian].