Second-order complex Newton root-finding algorithm for determining resonant modes of a nontrivial laser system

Design of a Model Reference Adaptive Controller Using Modified MIT Rule for a Second Order System

Sometimes conventional feedback controllers may not perform well online because of the variation in process dynamics due to nonlinear actuators, changes in environmental conditions and variation in the character of the disturbances. To overcome the above problem, this paper deals with the designing of a controller for a second order system with Model Reference Adaptive Control (MRAC) scheme usi...

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

On the property of for a second-order system with zero diagonal coefficient

Abstract: This paper investigates the problem of whether all trajectories of the system and cross the vertical isocline, which is very important for the existence of periodic solutions and oscillation theory. Sufficient conditions are given for all trajectories to cross the vertical isocline.  

A new family of four-step fifteenth-order root-finding methods with high efficiency index

‎In this paper a new family of fifteenth-order methods with high efficiency index is presented‎. This family include four evaluations of the function and one evaluation of its first derivative per iteration.‎ ‎Therefore‎, ‎this family of methods has the efficiency index which equals 1.71877‎. ‎In order to show the applicability and validity of the class‎, ‎some numerical examples are discussed‎.

Numerical method for a system of second order singularly perturbed turning point problems

In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...