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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Wright, Sarah"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dr. James V. Lambers","Dr. Haiyan Tian","Dr. Huiqing Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-12-01T08:00:00Z","date_published":"2020-12-01T08:00:00Z","updated_at":"2026-07-24T05:45:19Z","subjects":["Partial Differential Equations","Schrodinger Operators","Numerical Analysis and Computation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/785","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. James V. Lambers","Dr. Haiyan Tian","Dr. Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Wright, Sarah"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-10-10T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Partial Differential Equations","Schrodinger Operators","Numerical Analysis and Computation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/785"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials"]}]}],"canonical_facts":{"dc:contributor":["Dr. James V. Lambers","Dr. Haiyan Tian","Dr. Huiqing Zhu"],"dc:creator":["Wright, Sarah"],"dc:date.available":["2020-10-10T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/785"],"dc:subject":["Partial Differential Equations","Schrodinger Operators","Numerical Analysis and Computation"],"dc:title":["Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:19Z"}