Dynamic analysis of symmetric rotor with gyroscopic effect is performed in this study. First, equations of motion have been derived using Lagrange equation and then solved analytically by Homotopy Perturbation Method (HPM) and numerically appling Runge-Kutta-Fehlberg 4th-5th order method. Results are presented through graphs and table. Comparison of analytic outcomes with numerical ones showed ...

To my beautiful wife, Ashley. For your unconditional love, faithful encouragement, and resolute support. You have always believed in and inspired the pursuit of my dreams. iv ACKNOWLEDGEMENTS I would first like to express my immense gratitude to my advisor, Dr. Glenn Sjoden. What started as an undergraduate summer research project transformed into my path in graduate school. As both an advisor ...

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed ...

In this paper we propose Runge-Kutta Fehlberg method for solving fully fuzzy differential equations (FFDEs) of the form y ′ (t) = a⊗ y(t), y(0) = y0, t ∈ [0,T ] under strongly generalized H-differentiability. The algorithm used here is based on cross product of two fuzzy numbers. Using cross product we investigate the problem of finding a numerical approximation of solutions. The convergence of...

A device for electrostatic separation of triboelectrically charged plastic particles is modeled and optimized. Electric field in the system is solved numerically by a fully adaptive higher-order finite element method. The movement of particles in the device is determined by an adaptive Runge-Kutta-Fehlberg method. The shape optimization of the electrodes is carried out by a technique based on g...

The problem of thermal diffusion and diffusion thermo effects on thermosolutal Marangoni convection flow of an electrically conducting fluid over a permeable surface is investigated. Using appropriate similarity transformations, the governing system of partial differential equation is transformed to a set of nonlinear ordinary differential equations, then solved numerically using the Runge-Kutt...

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm cont...

The Kalman Filter (KF) is pervasively used to control a vast array of consumer, health and defense products. By grouping sets of symmetric state variables, the Relational Kalman Filter (RKF) enables us to scale the exact KF for large-scale dynamic systems. In this paper, we provide a parameter learning algorithm for RKF, and a regrouping algorithm that prevents the degeneration of the relationa...

We present software packages for the holonomic gradient method (HGM). These packages compute normalizing constants and the probabilities of some regions. While many algorithms which compute integrals over high-dimensional regions utilize the Monte-Carlo method, our HGM utilizes algorithms for solving ordinary differential equations such as the Runge-Kutta-Fehlberg method. As a result, our HGM c...

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involv...