Modeling of constrained motion

This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.

Boundary value problems for second order differential equations with $$\varphi $$-Laplacians

A new method for solving the boundary value problems for the second order ODEs with bounded nonlinearities and singular $$\varphi $$ φ –Laplacians is presented.

Fractional order differential calculus applied on decision making system to smart grid management via decision trees

This article portrays the relationship between fractional order differential calculus and the computational intelligence method, applying it to the improvement of intelligent systems. The Kirchhoff Laws, represented by second order differential equations, were solved via non-integer order differential calculus. The results obtained were used in the implementation of decision trees, which allowed the decision rules to be incorporated into the controllers. The results obtained by mathematical modeling did magnify the information extracted from Kirchhoff's Laws. Due to the gain magnitude of this information, the decision trees were obtained with greater precision and accuracy. In this way, it was achieved to build a hybrid system capable of being used in the development of controllers automata that has the lower response time and highest efficiency.

Convergence estimates for abstract second order differential equations with two small parameters and Lipschitzian nonlinearities

In a real Hilbert space $H$ we consider the following singularly perturbed Cauchy problem ... We study the behavior of solutions $u_{\varepsilon\delta}$ in two different cases: $\varepsilon\to 0$ and $\delta \geq \delta_0>0;$ $\varepsilon\to 0$ and $\delta \to 0,$ relative to solution to the corresponding unperturbed problem.We obtain some {\it a priori} estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of $t=0.$

Visualizing some numerical solutions of linear second order differential equations with the Euler method and Lagrange interpolation via GeoGebra

In this paper we will show the algebraic and graphic expressions, that were obtained through the Euler method and Lagrange interpolation by means of GeoGebra software for some linear second order differential equations. This teaching material was designed for the course of differential equations, and as a complement of support for the numerical calculation course for the engineering careers of the Universidad de Antofagasta.

Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r(t)(y′(t))α′=p(t)yα(τ(t)). Such differential equation may possesses two types of nonoscillatory solutions either from the class N0 (positive decreasing solutions) or N2 (positive increasing solutions). We establish new criteria for N0=∅ and N2=∅ provided that delayed and advanced parts of deviating argument are large enough. As a consequence of these results, we provide new oscillatory criteria. The presented results essentially improve existing ones even for a linear case of considered equations.