{"id":{"repo_id":"njit","oai_identifier":"oai:digitalcommons.njit.edu:dissertations-1967"},"canonical_url":"https://search.dev.ndltd.org/etd/njit/oai:digitalcommons.njit.edu:dissertations-1967","repository":{"repo_id":"njit","name":"NJIT","base_url":"https://digitalcommons.njit.edu/do/oai/"},"display":{"title":"Numerical detection of complex singularities in two and three dimensions","abstract":"Singularities often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. Our results generalize a well known method for the analysis of singularities in one-dimensional functions to higher dimensions. As an example, we apply this method to analyze the complex singularities for the 2D inviscid Burger's equation.","abstract_html":"Singularities often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. Our results generalize a well known method for the analysis of singularities in one-dimensional functions to higher dimensions. As an example, we apply this method to analyze the complex singularities for the 2D inviscid Burger's equation.","abstract_has_math":false,"creators":["Malakuti, Kamyar"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematical Sciences - (Ph.D.)","degree_level":null,"degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":["Michael Siegel","Russel E. Caflisch","Lou Kondic"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-05-31T07:00:00Z","date_published":"2009-05-31T07:00:00Z","updated_at":"2026-07-24T03:23:16Z","subjects":["Partial differential equation","Complex singularity","Burger equation","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.njit.edu/dissertations/912","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michael Siegel","Russel E. 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Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. Our results generalize a well known method for the analysis of singularities in one-dimensional functions to higher dimensions. As an example, we apply this method to analyze the complex singularities for the 2D inviscid Burger's equation."]},{"key":"dc:title","label":"Title","values":["Numerical detection of complex singularities in two and three dimensions"]}]}],"canonical_facts":{"dc:contributor":["Michael Siegel","Russel E. Caflisch","Lou Kondic"],"dc:creator":["Malakuti, Kamyar"],"dc:description.abstract":["Singularities often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in interfacial fluid dynamics such as Kelvin-Helmholtz instability, Rayleigh-Taylor instability, and Hele-Shaw flow. In this thesis, we present a new method for the numerical analysis of complex singularities in solutions to partial differential equations. In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. Our results generalize a well known method for the analysis of singularities in one-dimensional functions to higher dimensions. As an example, we apply this method to analyze the complex singularities for the 2D inviscid Burger's equation."],"dc:identifier":["https://digitalcommons.njit.edu/dissertations/912"],"dc:subject":["Partial differential equation","Complex singularity","Burger equation","Mathematics"],"dc:title":["Numerical detection of complex singularities in two and three dimensions"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_name":["Doctor of Philosophy in Mathematical Sciences - (Ph.D.)"]},"updated_at":"2026-07-24T03:23:16Z"}