Thesis Defense Announcement

The Herff College of Engineering announces the Final Thesis Defense of

Paul Koziel

for the Degree of Master of Science

on November 2, 2018 at 9:00 AM in Engineering Science Building, Room 317

Advisor: William S. Janna

Methods for Finding Zeros of the Kummer Function

ABSTRACT: An algorithm for determining the real eigenvalues of the confluent hypergeometric function known as the Kummer function is presented. There is a need for a large number of eigenvalues in order to describe developing flow in the classic Graetz problem. A numerical approach using the power series solution for the real portion of the Kummer function M(a; b; z) is implemented through a user-friendly MATLAB function. Methods of iterative root calculation using bisection, secant method, Newton's method, and Brent's method are considered. Combinations of methods for the classic Graetz problem are studied and implemented. Comparison with Graetz problem coefficients and eigenvalues published in the literature using a finite number of terms for the power series, exact solutions, as well as asymptotic approximations is provided to predict accuracy. The length of time needed to calculate a finite number of eigenvalues is measured and compared with that of other calculations published in the literature.