Date of Award
Fall 2020
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. James V. Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound speed changes. This means the variable related to the sound speed is not constant. We will modify this variable so that it is piecewise constant. The specific operator in this equation also makes current time-stepping methods not practical. The method used here will apply an eigenfunction expansion technique used in previous research that eliminates the current time-stepping problems.
Copyright
Wright, 2020
Recommended Citation
Wright, Sarah, "Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials" (2020). Master's Theses. 785.
https://aquila.usm.edu/masters_theses/785