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49 articles for “Linear Differential Equation”
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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 keywordsLeast Square Approximation by Linear Combination of Exponential FunctionsBahman Mehri, Dariush Shadman, Sadegh JokarHere we were concerned with least square approximation by exponential functions for given data. In this manuscript, we approximate the given data such that this approximant satisfies a differential equation. The case of nonlinear differential equations was also considered. …Journal of Mathematics and Statistics, Vol. 2, Issue 2 · 30 Jun 2006 · 6,875 accessesView PDFCite
Research ArticleOpen accessIn the abstractA 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 abstractDynamic Models for Rigid Memory MechanismsRelly Victoria Virgil PetrescuThe paper presents a dynamic model that works with variable internal damping, applicable directly to rigid memory mechanisms. If the problem of elasticity is generally solved, the problem of system damping is not clear and well-established. It is usually considered a constant "c" value for the internal damping of the system and sometimes the same value c and for the … …Journal of Mechatronics and Robotics, Vol. 3, Issue 1 · 6 May 2019 · 5,981 accessesView PDFCite
Research ArticleOpen accessIn the abstractPitch Control of a Rocket with a Novel LQG/LTR Control AlgorithmAliyu Bhar Kisabo, Aliyu Funmilayo Adebimpe, Sholiyi Olusegun SamuelThis paper presents the design, simulation and analysis of a novel LQG and LQG/LTR control algorithm for the pitch angle of a sounding rocket. These improved LQG and LQG/LTR control algorithms stem from the fact that a Riccati Differential Equation (RDE) rather than the popular Algebraic Riccati Equation (ARE) is used to obtaining the Kalman gain in the observer of … …Journal of Aircraft and Spacecraft Technology, Vol. 3, Issue 1 · 12 Mar 2019 · 7,366 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
Research ArticleOpen accessIn the abstractExact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard TypeLucas H. Koudahoun, Jean Akande, Damien K.K. Adjaï et al.Authors introduce a generalized singular differential equation of quadratic Liénard type for study of exact classical and quantum mechanical solutions. The equation is shown to exhibit periodic solutions and to include the linear harmonic oscillator equation and the Painlevé-Gambier XVII equation as special cases. It is also shown that the equation may exhibit discrete eigenstates as quantum behavior under Nikiforov-Uvarov … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 5 Jul 2018 · 7,609 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn Almost Periodic Solutions of Abstract Semilinear Fractional Inclusions with Weyl-Liouville Derivatives of Order γ ∈ (0, 1]Marko KostićThe main aim of this paper is to examine the existence and uniqueness of almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. We deal with the Weyl-Liouville fractional derivatives of order γ ∈ (0, 1], paying special attention to the analysis of semilinear differential inclusions of first order. We use the results … …Journal of Mathematics and Statistics, Vol. 13, Issue 3 · 26 Jul 2017 · 6,787 accessesView PDFCite
Research ArticleOpen accessIn the abstractFree Vibration Analysis of Rectangular Cantilever Plates Using the Hyperbolic-Trigonometric SeriesMikhail V. Sukhoterin, Sergey O. Baryshnikov, Dmitry A. AksenovThe purpose of this paper is to develop a numerical analytical method for an accurate solution to the problem on frequencies and mode shapes of a rectangular cantilever plate. The problem is reduced to an infinite system of linear algebraic equations relative to ratios of trigonometric series, which contains vibration frequency as a parameter. The core of the method is … …American Journal of Applied Sciences, Vol. 13, Issue 12 · 23 Dec 2016 · 7,283 accessesView PDFCite
Research ArticleOpen accessIn the abstractNew Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential EquationsRa’ft Abdelrahim, Zurni Omar, John Olusola KuboyeA new single-step hybrid block method with three off-step points for the solution of first order ordinary differential equations is proposed. The strategy employed to develop this method is interpolating the power series approximate solution at xn and off-step points and collocating the derivative of the power at xn+1. The class of linear multistep method derived is then simultaneously applied … …American Journal of Applied Sciences, Vol. 13, Issue 2 · 18 Feb 2016 · 8,234 accessesView PDFCite