| Abstract: | Schemes that are free of the disadvantages of both the finite-difference and finite-element methods and retain the advantages
of the saturation-free grid methods are proposed and investigated. The asymptotic behavior of their maximal N th eigenvalue
is the same as the behavior of the N the eigenvalue of a differential operator, and it is not difficult to apply these discretizations
to nonstationary problems. In contrast to polynomial pseudospectral approximations, the schemes of this paper, as well as
of E. B. Karpilovskaya, “Convergence of the collocation method,” Sov. Math. Dokl.,4, No. 2, 1070–1073 (1963) and I. P. Gavrilyuk and L. D. Grekov, On Algorithms for the Realization of Grid Schemes without
the Accuracy Staturation for Second-Order Ordinary Differential Equations in Russian], Deposited at UkrNIINTI 16.08.1991,
utilize uniform grids. Bibliography: 27 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 78, 1994, pp. 1–27. |
