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61 articles for “Nonlinear equations”
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Research ArticleOpen accessIn the keywordsA Cartesian Regulator for an Ideal Position-Servo Actuated Didactic Mechatronic Device: Asymptotic Stability AnalysisGabriela Zepeda, Rafael Kelly, Carmen MonroyPosition-servo actuators are by themselves feedback mechatronics systems modeled by Ordinary Differential Equations (ODE). From a technological point of view, position-servos are based upon an electrical motor, a shaft angular position sensor, and a dominant Proportional controller. These position servo actuators are at the core of several real-life practical and didactic mechatronics and robotics systems. The contribution of this study … …American Journal of Engineering and Applied Sciences, Vol. 15, Issue 3 · 16 Sep 2022 · 5,821 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential EquationsMykola YaremenkoThis article is dedicated to expanding our comprehension of the regularity of the solutions to the Cauchy problem for the quasilinear second-order parabolic partial differential equations under fair general conditions on the nonlinear perturbations. In this paper have been obtained that the sequence of the weak solutions uz ∈ V1,02, z = 1,2,..... to the Cauchy problems for the Equations … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 2 Jun 2020 · 7,282 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph ColoringHaridas Kumar Das, Nasim RezaThis paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 27 Jun 2018 · 8,591 accessesView PDFCite
Research ArticleOpen accessIn the keywordsApplication of an Enhanced (G'/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Particle PhysicsS.M. Rayhanul IslamThe enhanced (G'/G)-expansion method is very effective and powerful method to find the exact traveling wave solutions of nonlinear evolution equations. We choose the Phi-4 equation to illustrate the validity and advantages of this method. As a result, many exact traveling wave solutions are obtained, which include soliton, hyperbolic function and trigonometric function solutions. …American Journal of Applied Sciences, Vol. 12, Issue 11 · 13 Nov 2015 · 7,037 accessesView PDFCite
Research ArticleOpen accessIn the keywordsLagrange II Dynamics and that of Forces Exemplified on a Basic Robot, 2 DoFRelly Victoria Virgil PetrescuThe paper presents two dynamic methods applied to a basic articulated robot, 2 DoF, the first being an original adaptation of the type II Lagrange equations and the second being a dynamic method based on the influence of the forces in the robot mechanism. Both methods are original, as they were designed and applied by the author to a 2 … …American Journal of Engineering and Applied Sciences, Vol. 16, Issue 2 · 26 Jul 2023 · 5,752 accessesView PDFCite
Research ArticleOpen accessIn the keywordsAnalytical Solution of Nonlinear Vibrating SystemsN. Tolou, I. Khatam, B. Jafari, D. D. GanjiThe responses of nonlinear vibrating systems are investigated analytically using Homotopy Perturbation Method (HPM). To demonstrate the validity of the proposed method, the results obtained by HPM have been depicted graphically and have been compared with those of the exact solution. A clear conclusion can draw from the numerical results that the method provides highly accurate solutions to the discussed … …American Journal of Applied Sciences, Vol. 5, Issue 9 · 30 Sep 2008 · 7,149 accessesView PDFCite
Research ArticleOpen accessIn the keywordsFlow of Temperature-dependent Viscous Fluid Between Parallel Heated Walls: Exact Analytical Solutions in the Presence of Viscous DissipationK. S. Adegbie, F. I. AlaoWe examine steady incompressible flow of viscous liquids between parallel heated walls of plane Couette device. The temperature of the upper and lower walls of the device are maintained at T = Tb and T = T0 respectively. Of a particular interest are exact analytical solutions of the coupled non-linear differential equations resulting from plane Couette flow obtained for the … …Journal of Mathematics and Statistics, Vol. 3, Issue 1 · 31 Mar 2007 · 7,480 accessesView PDFCite
Research ArticleOpen accessIn the keywordsRegionalization Method for Nonlinear Differential Equation Systems In a Cartesian PlanBelaib LekhmissiWe propose a regionalization technique for analyzing nonlinear differential equation systems where coefficients are standard and nonzero. The present work starts with the study of a natural object which was the magic squares providing us with a new way to partition the plan in regions. …Journal of Mathematics and Statistics, Vol. 2, Issue 4 · 31 Dec 2006 · 6,069 accessesView PDFCite
Research ArticleOpen accessIn the abstractState-Space Modelling of a Rocket for Optimal Control System DesignAliyu Bhar Kisabo, Aliyu Funmilayo Adebimpe, Odooh Clement Okwo, Sholiyi Olusegun SamuelIn this study, we present the derivation of the mathematical model for a rocket’s autopilot in state-space. The basic equations defining the airframe dynamics of a typical six-Degree-of-Freedom (6DoF) are non-linear and coupled. Separation of these nonlinear coupled dynamics is presented as lateral and longitudinal dynamic equations. The need to determine aerodynamic coefficients and there derivative components are brought to … …Journal of Aircraft and Spacecraft Technology, Vol. 3, Issue 1 · 25 May 2019 · 13,632 accessesView PDFCite
Research ArticleOpen accessIn the abstractSolutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman TransformationDamien Kolawolé Kêgnidé Adjaï, Lucas Hervé Koudahoun, Jean Akande et al.A new approach using the generalized Sundman transformation to solve explicitly and exactly in a straightforward manner the cubic elliptic Duffing equation is proposed in this study. The method has the advantage to closely relate this equation to the linear harmonic oscillator equation and to be applied to solve other nonlinear differential equations. As a result, explicit and exact general … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 8 Nov 2018 · 7,251 accessesView PDFCite