Graduation Semester and Year

2013

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Benito Chen-Charpentier

Abstract

The role of randomness in mathematical models is of paramount importance, with emphasis placed upon the accuracy and reliability of predictions a rational approach is the use of differential equations with random parameters to describe natural phenomena. Well known methods such as Monte Carlo methods and the method of moments have been implemented to approximate the solutions to random differential equations in the last few decades. In this work, analytic solutions to a particular Riccati type dierential equation and discrete delay dierential equation with random coefficients are derived, also, due to its spectral rate of convergence and simplicity, the polynomial chaos expansion method is considered to approximate the moments of the solutions. The performance of the method is exhibited and potential future applications are discussed.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Mathematics Commons

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