{"id":{"repo_id":"wayne-thes","oai_identifier":"oai:digitalcommons.wayne.edu:oa_dissertations-1132"},"canonical_url":"https://search.dev.ndltd.org/etd/wayne-thes/oai:digitalcommons.wayne.edu:oa_dissertations-1132","repository":{"repo_id":"wayne-thes","name":"Wayne State University","base_url":"https://digitalcommons.wayne.edu/do/oai/"},"display":{"title":"Spectral Methods For The Hamiltonian Systems","abstract":"<p>We conduct a systematic comparison of spectral methods with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> <p>both energy and symplectic structure up to the machine error in each</p> <p>time (large) step, and therefore has a better long time behavior.</p>","abstract_html":"&lt;p&gt;We conduct a systematic comparison of spectral methods with some&lt;/p&gt; &lt;p&gt;symplectic methods in solving Hamiltonian dynamical systems. Our&lt;/p&gt; &lt;p&gt;main emphasis is on the non-linear problems. Numerical evidence has&lt;/p&gt; &lt;p&gt;demonstrated that the proposed spectral collocation method preserves&lt;/p&gt; &lt;p&gt;both energy and symplectic structure up to the machine error in each&lt;/p&gt; &lt;p&gt;time (large) step, and therefore has a better long time behavior.&lt;/p&gt;","abstract_has_math":false,"creators":["Kanyamee, Nairat"],"institution":null,"degree_name":"Ph.D.","degree_level":"Open Access Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["ZHIMIN ZHANG"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T05:58:42Z","subjects":["COLLOCATION METHODS","HAMILTONIAN SYSTEM","NUMERICAL METHODS","SPECTRAL METHODS","Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wayne.edu/oa_dissertations/133","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["ZHIMIN ZHANG"]},{"key":"dc:creator","label":"Author","values":["Kanyamee, Nairat"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2011-10-21T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["COLLOCATION METHODS","HAMILTONIAN SYSTEM","NUMERICAL METHODS","SPECTRAL METHODS","Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wayne.edu/oa_dissertations/133"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We conduct a systematic comparison of spectral methods with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> <p>both energy and symplectic structure up to the machine error in each</p> <p>time (large) step, and therefore has a better long time behavior.</p>"]},{"key":"dc:title","label":"Title","values":["Spectral Methods For The Hamiltonian Systems"]}]}],"canonical_facts":{"dc:contributor":["ZHIMIN ZHANG"],"dc:creator":["Kanyamee, Nairat"],"dc:date.available":["2011-10-21T07:00:00Z"],"dc:description.abstract":["<p>We conduct a systematic comparison of spectral methods with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> <p>both energy and symplectic structure up to the machine error in each</p> <p>time (large) step, and therefore has a better long time behavior.</p>"],"dc:identifier":["https://digitalcommons.wayne.edu/oa_dissertations/133"],"dc:subject":["COLLOCATION METHODS","HAMILTONIAN SYSTEM","NUMERICAL METHODS","SPECTRAL METHODS","Applied Mathematics"],"dc:title":["Spectral Methods For The Hamiltonian Systems"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-24T05:58:42Z"}