Physical Sciences and Mathematics Commons^™

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

Solving Differential Equations With Least Square And Collocation Methods, Katayoun Bodouhi Kazemi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this work, we first discuss solving differential equations by Least Square Methods (LSM). Polynomials are used as basis functions for first-order ODEs and then B-spline basis are introduced and applied for higher-order Boundary Value Problems (BVP) and PDEs. Finally, Kansa's collocation methods by using radial basis functions are presented to solve PDEs numerically. Various numerical examples are given to show the efficiency of the methods.

Mathematical Equations And System Identification Models For A Portable Pneumatic Bladder System Designed To Reduce Human Exposure To Whole Body Shock And Vibration, Ezzat Aziz Ayyad

UNLV Theses, Dissertations, Professional Papers, and Capstones

A mathematical representation is sought to model the behavior of a portable pneumatic foam bladder designed to mitigate the effects of human exposure to shock and whole body random vibration. Fluid Dynamics principles are used to derive the analytic differential equations used for the physical equations Model. Additionally, combination of Wiener and Hammerstein block oriented representation techniques have been selected to create system identification (SID) block oriented models. A number of algorithms have been iterated to obtain numerical solutions for the system of equations which was found to be coupled and non-linear, with no analytic closed form solution. The purpose …

Estimation Of Travel Time Based On Vehicle-Tracking Models, Anuj Nayyar

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we study the travel time problem based on the known traffic density model. Using the conservation law, we model the travel time function by a boundary value problem of a non homogeneous linear hyperbolic equation. The equation is transformed into an initial value hyperbolic equation, and the well-posedness of the problem is discussed. The mathematical analysis for both density and travel problems are given. We also derive the analytic solutions for several special cases of traffic density. Numerical schemes are proposed for solving for travel time problem. Several numerical examples are presented and error analysis on the …

Stability Aware Delaunay Refinement, Bishal Acharya

UNLV Theses, Dissertations, Professional Papers, and Capstones

Good quality meshes are extensively used for finding approximate solutions for partial differential equations for fluid flow in two dimensional surfaces. We present an overview of existing algorithms for refinement and generation of triangular meshes. We introduce the concept of node stability in the refinement of Delaunay triangulation. We present two algorithms for generating stable refinement of Delaunay triangulation. We also present an experimental investigation of a triangulation refinement algorithm based on the location of the center of gravity and the location of the center of circumcircle. The results show that the center of gravity based refinement is more effective …

Hardware-Software Co-Design, Acceleration And Prototyping Of Control Algorithms On Reconfigurable Platforms, Desta Kumsa Edosa

UNLV Theses, Dissertations, Professional Papers, and Capstones

Differential equations play a significant role in many disciplines of science and engineering. Solving and implementing Ordinary Differential Equations (ODEs) and partial Differential Equations (PDEs) effectively are very essential as most complex dynamic systems are modeled based on these equations. High Performance Computing (HPC) methodologies are required to compute and implement complex and data intensive applications modeled by differential equations at higher speed. There are, however, some challenges and limitations in implementing dynamic system, modeled by non-linear ordinary differential equations, on digital hardware. Modeling an integrator involves data approximation which results in accuracy error if data values are not considered …

Periodic Solutions And Positive Solutions Of First And Second Order Logistic Type Odes With Harvesting, Cody Alan Palmer

UNLV Theses, Dissertations, Professional Papers, and Capstones

It was recently shown that the nonlinear logistic type ODE with periodic harvesting has a bifurcation on the periodic solutions with respect to the parameter ε:

u' = f (u) - ε h (t).

Namely, there exists an ε0 such that for 0 < ε < ε0 there are two periodic solutions, for ε = ε0 there is one periodic solution, and for ε >ε0 there are no periodic solutions, provided that....

In this paper we look at some numerical evidence regarding the behavior of this threshold for various types of harvesting terms, in particular we find evidence in the negative or a conjecture regarding the behavior of this threshold value.

Additionally, we look at analagous steady states for the reaction-diusion …