Newton’s method and its variants are among the most efficient methods known for solving systems of non-linear equations when the functions involved are continuously differentiable. Besides its practical applications, Newton’s method is also a powerful theoretical tool. Therefore, it has been studied and used extensively. One of the famous results on Newton’s method is the well-known Kantorovich...

A semi-analytical approach to the elastic nonlinear stability analysis of rectangular plates is developed. Arbitrary boundary conditions and general out-of-plane and in-plane loads are considered. The geometrically nonlinear formulation for the elastic rectangular plate is derived using the thin plate theory with the nonlinear von Kármán strains and the variational multi-term extended Kantorovi...

The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the Lagrangian L(v, x, t) from the set of orbits in Rn to a set of measure-valued orbits. The Eulerian, dual formulation leads an optimization problem on the set of sub-solutions of the corresponding Hamilton-Jacobi equation. Finally, the Monge proble...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

This paper concerned with applicability of the method of Kantorovich majorants to nonlinear singular integral equations with Hilbert kernel . The results are illustrated in Hölder space. RESUMEN Este art́ıculo es concerniente a la aplicabilidad del método de mayorantes de Kantorovich para ecuaciones integrales singulares no lineales con núcleo de Hilbert. Los resultados son aplicaciones en espac...

First time, an analytical two-dimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constitutive relations, governing partial differential equations (PDEs) is obtained by employing Ressiner mixed var...