In the present paper, we deal with approximation properties of semi-exponential Sz?sz-Mirakyan-Kantorovich operators. Here, establish relation between Sz?sz-Mirakyan operators and its Kantorovich variant. Further, propose modification variant so as to preserve test functions eAx e2Ax derive Voronovskaya-type result.

This review surveys a significant set of recent ideas developed in the study of nonlinear Galerkin approximation. A significant role is played by the Krasnosel’skii Calculus, which represents a generalization of the classical inf-sup linear saddle point theory. A description of a proper extension of this calculus, and the relation to the inf-sup theory are part of this review. The general study...

We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2-Hermite-elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain veriied bound...

The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached given system. Finally Newton-Kantorovich iterations regained.

We establish necessary and sufficient conditions for the solvability of nonlinear boundary-value problem in critical case develop a scheme construction solutions this problem. By using Newton–Kantorovich method, we propose new iterative determination to weakly system ordinary differential equations case. As examples application constructed scheme, obtain approximations periodic Duffing Lienard ...