COLLEGE OF ARTS & SCIENCES
and in each column p times, and any pair of different symbols occur together q times. Understanding trivial examples, the properties, and the math behind the problem reveals multiple examples and a systematic way to build generalized multi-latin squares.
An Aronszajn Tree
STUDENTS Chester E Lian ADVISORS Lynne C Yengulalp LOCATION, TIME RecPlex, 11:00 AM-12:30 PM Mathematics, Poster - Honors Thesis Contrary to the popular belief that “infinity is not a number; it’s a concept,” numbers that are not finite do exist. Mathematicians call them transfinite numbers. Just like ordinary numbers, some transfinite numbers are larger than others. This can be thought of as there being different levels of infinity, where some infinities are “more infinite” than others. If we draw a family tree in which every generation has finitely many offspring, and every chain of descendants is finite, then it is clear that we cannot have infinitely many family members. In the realm of the transfinite, things are not as intuitive: If we draw a family tree in which every generation has offspring at a certain level of infinity, and every chain of descendants is at that same level of infinity, it is possible (though not necessary) that the total number of family members is at a higher level of infinity.
Exploring the Sinc-Collocation Method for Solving the Integro-Differential Equation
STUDENTS Han Li ADVISORS Muhammad Usman LOCATION, TIME RecPlex, 11:00 AM-12:30 PM Mathematics, Poster - Course Project, 13 SP MTH 556 01 In this project we study the Sinc approximation method to solve a family of integral differential equations. First we will apply the Sinc-collocation method to solve the second order Fredholm integro-differential equation. Numerical results and examples demonstrate the reliability and efficiency of this method. Secondly, various types of integro-differential equations are solved by Sinc-collocation technique and the numerical results are compared, to explore the stability of this method.
Numerical solution of the KdV equation with periodic boundary conditions using the sinc-collocation method
STUDENTS Nicholas D. Haynes ADVISORS Muhammad Usman LOCATION, TIME RecPlex, 11:00 AM-12:30 PM Mathematics, Poster - Graduate Research We demonstrate numerically the eventual time-periodicity of the solutions of the Korteweg-de Vries equation with periodic forcing at the boundary using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third-order boundary value problem. The first-order time derivative is approximated with a weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem.
Simulation of Nonlinear Waves Using Sinc Collocation-Interpolation
STUDENTS Eric A Gerwin, Jessica E Steve ADVISORS Muhammad Usman LOCATION, TIME RecPlex, 11:00 AM-12:30 PM Mathematics, Poster - Course Project, 13 SP MTH 556 01 In this project we explore the Sinc collocation method to solve an initial and boundary valueproblem of nonlinear wave equation. The Sinc collocation method is based uponinterpolation technique, by discretizing the function and its spatial derivatives usinglinear combination of translated Sinc functions. Our project will focus on multipleboundary conditions such as the well known Dirichlet and Neumann conditions. Ourproject will also focus on two established nonlinear partial differential equations: theSine-Gordon equation and the Kortweg-de Vries equation.
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