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 ...

In this paper, a new algorithm for solving cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) for weakly coupled large-scale systems is proposed. It is shown that since the proposed algorithm is based on the Newton’s method, the quadratic convergence is attained. Moreover, the local uniqueness of the convergence solutions for the CSAREs is investigated. Finally, in order to over...

The problem of finding all intersections between two surfaces has many applications in computational geometry and computer-aided geometric design. We propose an algorithm based on Newton’s method and subdivision for this problem. Our algorithm uses a test based on the Kantorovich theorem to prevent the divergence or slow convergence problems normally associated with using unsuitable starting po...

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...

In this paper, we present a global convergence theory for Newton's Method in n dimensions for functions of polynomial character (generic or truncated Taylor series), augmenting the classical Newton-Kantorovich results on quadratic convergence. It is shown that there exist ve distinct, quantiiable convergence states, which can be described by a nite state machine. From this convergence descripti...