Ordinary Differential Equations and Applied Dynamics Commons^™

Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim

Theses, Dissertations and Capstones

Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical …

Mechanical Visualization Of A Second Order Dynamic Equation On Varying Time Scales, Molly Kathryn Peterson

Theses, Dissertations and Capstones

In this work, we give an introduction to Time Scales Calculus, the properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equation of second order. Time Scales Calculus was introduced by Stefan Hilger in 1988. It brings together the theories of difference and differential equations into one unified theory. By using the properties of the delta derivative and the delta anti-derivative, we analyze the behavior of a second order linear homogeneous dynamic equation on various time scales. After the analytical discussion, we will graphically evaluate the second order dynamic equation in Marshall’s …

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Theses, Dissertations and Capstones

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …

Twin Solutions Of Even Order Boundary Value Problems For Ordinary Differential Equations And Finite Difference Equations, Xun Sun

Theses, Dissertations and Capstones

The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem

(-1)ⁿy⁽²ⁿ⁾ = f(y); n = 1; 2; 3 ... and t 2 [0; 1];

with boundary conditions

y(2k)(0) = 0

y^(2k+1)(1) = 0 for k = 0; 1; 2 ... n - 1:

This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem

(-1)^{n (2n)}u(k)g(u(k)); n = 1; 2; 3 .... and k (0; ... N);

with boundary conditions

(2k)u(0) …

A Study Of Present Value Maximization For The Monopolist Problem In Time Scales, Keshav Prasad Pokhrel

Theses, Dissertations and Capstones

There are some mathematical characters in the abstract that will not transfer. Refer to the download to read full abstract.

General results for time scales with right dense points are established. A study of issues that arise when unifying (C) and (D) is included in the analysis