In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

The technique of applying the criterion of approximate monotonicity is shown. An example of the selection of technological parameters (conditions of friction and degree of deformation) of drawing with thinning, providing an approximate monotonicity of the process, is given. Keywords monotonic deformation, monotonicity condition, approximate monotonicity criterion, application of the approximate monotonicity criterion, drawing with wall thinning. remshev@mail.ru

Beam-like structures are widespread but essential systems that have been extensively studied for centuries. Although several proposed solutions are effective, the time consumption and the difficulty of reconstructing the problem are the major disadvantages of these methods. This paper offers a new methodology for finding solutions to beam problems based on Machine Learning and Neural Networks with different optimization algorithms. Various regression models are compared on numerically stimulated Euler-Bernoulli beam modelling.

The aim of this paper is to extend and generalize Picard-Green’s fixed point iteration method for the solution of fourth-order Boundary Value Problems. Several numerical applications to linear and nonlinear fourth-order Boundary Value Problems are discussed to illustrate the main results.