Physical Sciences and Mathematics Commons^™

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) …

Variable Shape Parameter Strategies In Radial Basis Function Methods, Derek Sturgill

Theses, Dissertations and Capstones

The Radial Basis Function (RBF) method is an important tool in the interpolation of multidimensional scattered data. The method has several important properties. One is the ability to handle sparse and scattered data points. Another property is its ability to interpolate in more than one dimension. Furthermore, the Radial Basis Function method provides phenomenal accuracy which has made it very popular in many fields. Some examples of applications using the RBF method are numerical solutions to partial differential equations, image processing, and cartography. This thesis involves researching Radial Basis Functions using different shape parameter strategies. First, we introduce the Radial …