Publication Date

6-15-2021

Document Type

Thesis

Degree Name

Master of Science in Mathematics (MS)

Committee Member

Goonatilake, Rohitha H

Committee Member

Makaya, Jacob S.

Committee Member

Hinojosa, Juan H

Abstract

In this thesis, we will be presenting new symmetric Gaussian quadrature rules over the triangle for orders 3, 4, 5, and 6 that have positive weights and nodes that are within the integration domain. In addition to this, we will compare these rule with those found in the literature, specifically by Witherden and Vincent [17], by computing their Lebesgue constants and determining which has the lowest. In order to accomplished these goals, we will go over the theory behind Gaussian quadrature and barycentric coordinates, the coordinate system that will be used in representing our rules. The process by which one derives a quadrature rule involves solving a nonlinear system of equations. For this reason, we will go over Newton’s method and the Gauss-Newton method. We will then go over the Lebesgue constant, first for the general simplex S^m and then for the triangle S^2. Lastly, we will present our rules and compare them with those from [17].

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