43 articles for “Ordinary Differential Equation”

Research ArticleOpen accessIn the keywordsA Repairable System with N Failure Modes and K Standby Units Using Separation of Variable MethodKh. M. El-Said, N. A. AginaThis study deals with a repairable system with N failure modes and K standby unit. Using separation of variable method by solving linear ordinary differential equation for system equations obtained by using the supplementary variable method. …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 6,113 accessesView PDF Cite

Research ArticleOpen accessIn the keywordsA New Perturbative Approach in Nonlinear Singularity AnalysisTat-Leung YeeProblem statement: The study is devoted to the “mirror” method which enables one to study the integrability of nonlinear differential equations. Approach: A perturbative extension of the mirror method is introduced. Results: The mirror system and its first perturbation are then utilized to gain insights into certain nonlinear equations possessing negative Fuchs indices, which were poorly understood in the literatures. … …Journal of Mathematics and Statistics, Vol. 7, Issue 3 · 29 Jul 2011 · 7,334 accessesView PDF Cite

Research ArticleOpen accessIn the abstractUnicycle Robot’s Navigation Control with Obstacle Avoidance and Asymptotic StabilityJuan Andrés Roteta Lannes, Andres Gabriel GarciaThis study builds upon the groundbreaking research of Asymptotic stability of unicycle-like robots with the Bessel’s controller continuing the exploration of asymptotic stability for non-holonomic robots through kinematic modeling that allows for obstacle avoidance. utilizing the previously derived Bessel's controller, the study defines an avoidance region containing obstacles, presenting an algorithm that relies solely on the distance to the obstacle. … …American Journal of Engineering and Applied Sciences, Vol. 17, Issue 1 · 28 Feb 2024 · 5,045 accessesView PDF Cite

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 · 5,825 accessesView PDF Cite

Research ArticleOpen accessIn the abstractHeat Generation/Absorption Effect on Natural Convection Flow in a Vertical Annulus with Time-Periodic Boundary ConditionsMichael O. Oni, Basant K. JhaThe role of heat generation/absorption on natural convection flow formation in a vertical annulus with prescribed time-periodic heating is investigated in this article. The governing continuity, momentum and energy equations are converted into ordinary differential equation using suitable transformations and closed form expressions are obtained for temperature distribution, velocity profile, Nusselt number, skin friction and mass flow rate in terms … …Journal of Aircraft and Spacecraft Technology, Vol. 3, Issue 1 · 27 Jul 2019 · 6,340 accessesView PDF Cite

Research ArticleOpen accessIn the abstractFitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value ProblemsAsad Freihat, Radwan Abu-Gdairi, Hammad Khalil et al.In this article, the reproducing kernel Hilbert space W24 [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The … …American Journal of Applied Sciences, Vol. 13, Issue 5 · 11 May 2016 · 7,654 accessesView PDF Cite

Research ArticleOpen accessIn the abstractFREE CONVECTION OF HEAT TRANSFER IN FLOW PAST A SEMI-INFINITE FLAT PLATE IN TRANSVERSE MAGNETIC FIELD WITH HEAT FLUXP. Geetha, M.B.K. Moorthy, M. DakshinamoorthyA steady two-dimensional MHD free convection of heat transfer in flow past a semi-infinite flat plate in transverse magnetic field with heat flux has been examined. The governing partial differential equation are non-dimensionalised and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable η and using Runge-Kutta Gill method with shooting technique. The velocity … …American Journal of Applied Sciences, Vol. 11, Issue 9 · 4 Jul 2014 · 7,064 accessesView PDF Cite

Research ArticleOpen accessIn the abstractUNSTEADY BOUNDARY LAYER FLOW ALONG A STRETCHING CYLINDER AN ANALYTICAL SOLUTIONM. Y. AklThe axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless … …Journal of Mathematics and Statistics, Vol. 10, Issue 2 · 17 Feb 2014 · 7,155 accessesView PDF Cite

Research ArticleOpen accessIn the abstractA Non-Linear Absolutely-Stable Explicit Numerical Integration Algorithm for Stiff Initial-Value ProblemsEssam R. El-ZaharThe time-step in integration process has two restrictions. The first one is the time step restriction due to accuracy requirement τac and the second one is the time-step restriction due to stability requirement τst. The most of explicit methods have small stability regions and consequently small τst. It obliges us to solve stiff problems with small step size τst << … …American Journal of Applied Sciences, Vol. 10, Issue 11 · 11 Sep 2013 · 7,565 accessesView PDF Cite

Research ArticleOpen accessIn the abstractApplication of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in PoultryUdofia Ekere Sunday, Inyama Simeon ChiomaProblem statement: In this study, we present the mathematical model of the transmission dynamics of fowl pox infection in poultry. Approach: It describes the interaction between the susceptible and the infected birds which results in a system of ordinary differential equation. Introducing the control which represents the effort in applying chemoprophylaxis control u1 and treatment control u2 in birds with … …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 13 Jun 2012 · 6,957 accessesView PDF Cite