Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 21 for “"Ordinary Differential Equations and Applied Dynamics"”.
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Three Methods for Solving the Low Energy Neutron Boltzmann Equation
… component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two non-coupled integro-differential equations describing both forward and backward …
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On the Evolution of Virulence
<p>The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear …
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An Adaptive Method for Calculating Blow-Up Solutions
… such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, <em>ad hoc</em> methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having <em>a priori</em> …
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On the Complexity of Computing Galois Groups of Differential Equations
<p>The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic …
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Green's Functions of Discrete Fractional Calculus Boundary Value Problems and an Application of Discrete Fractional Calculus to a Pharmacokinetic Model
… the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction …
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A Generalization of Linear Multistep Methods
… that are currently available to solve systems of ordinary differential equations is made. This generalization is made by constructing linear multistep methods from an arbitrary set of monotone interpolating and approximating functions. Local truncation error estimates as well as stability analysis …
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A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations
… solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration …
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A Novel Mathematical Model of the Trojan Y-Chromosome Strategy with Optimal Control
… problem all over the world. Controlling and eradicating an invasive species is an even more diffcult problem. The Trojan Y Chromosome (TYC) eradication strategy is one control method. This method alters the female to male sex ratio by introducing sex reversed males called supermales. …
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A Forward-Backward Fluence Model for the Low-Energy Neutron Boltzmann Equation
… equation was separated into two coupled integro-differential equations describing forward and backward neutron fluence in selected materials. Linear B-splines were used to change the integro-differential equations into a coupled system of ordinary differential equations (O.D.E.'s). Difference …
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A survey of mathematical models of Dengue fever
<p>In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model</p>
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Minimizing Travel Time Through Multiple Media With Various Borders
… of two main chapters along with an introduction and<br />conclusion. In the introduction, we address the inspiration for the thesis, which<br />originates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss …
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Theoretical Analysis of Nonlinear Differential Equations
<p>Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, …
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Smarticles: A Method for Identifying and Correcting Instability and Error Caused by Explicit Integration Techniques in Physically Based Simulations
… has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of …
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Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems
<p>In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It …
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Rotordynamic Analysis of Theoretical Models and Experimental Systems
… fundamental information for the construction and</p> <p>analysis of rotordynamic theoretical models, and their comparison the experimental</p> <p>systems. Finite Element Method (FEM) is used to construct models using Timoshenko</p> <p>beam elements with viscous and hysteretic internal damping. …
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Modelling Β2Ar Regulation
… smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory …
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Dual Quaternions for Gravity Recovery Missions
… dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to …
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Rigid Body Constrained Motion Optimization and Control on Lie Groups and Their Tangent Bundles
… motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and …
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Proof-of-Concept For Converging Beam Small Animal Irradiator
… TOPAS, the multiphysics solver COMSOL., and</p> <p>several analytical radiation transport methods were employed to perform an in-depth proof-ofconcept</p> <p>for a high dose rate, high precision converging beam small animal irradiation platform.</p> <p>In the first aim of this work, a …
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