The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	Numerical detection of complex singularities in two and three dimensions
Author:	Malakuti, Kamyar
View Online:	njit-etd2009-060 (x, 74 pages ~ 4.6 MB pdf)
Department:	Department of Mathematical Sciences
Degree:	Doctor of Philosophy
Program:	Mathematical Sciences
Document Type:	Dissertation
Advisory Committee:	Siegel, Michael (Committee chair) Caflisch, Russel E. (Committee member) Kondic, Lou (Committee member) Luke, Jonathan H.C. (Committee member) Papageorgiou, Demetrius T. (Committee member)
Date:	2009-05
Keywords:	Partial differential equation Complex singularity Burger equation
Availability:	Unrestricted
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.