Inverse Sturm-Liouville Systems over the whole Real Line

Altundağ, Hüseyin
In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization techniques to overcome the ill-posedness difficulty. Moreover, since the problem is nonlinear the iterative solution procedures are needed. Direct computation of the eigenvalues in iterative solution is handled via psoudespectral methods. The numerical examples of the considered problem are given to illustrate the accuracy and convergence behaviour.


Two dimensional finite volume weighted essentially non-oscillatory euler schemes with uniform and non-uniform grid coefficients
Elfarra, Monier Ali; Akmandor, İbrahim Sinan; Department of Aerospace Engineering (2005)
In this thesis, Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) codes for one and two-dimensional discretised Euler equations are developed. The construction and application of the FV-WENO scheme and codes will be described. Also the effects of the grid coefficients as well as the effect of the Gaussian Quadrature on the solution have been tested and discussed. WENO schemes are high order accurate schemes designed for problems with piecewise smooth solutions containing discontinuities. The key ...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
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Eraslan, Elvan; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2006)
This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe’s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruc...
Local operator spaces, unbounded operators and multinormed C*-algebras
Dosiev, Anar (Elsevier BV, 2008-10-01)
In this paper we propose a representation theorem for local operator spaces which extends Ruan's representation theorem for operator spaces. Based upon this result, we introduce local operator systems which are locally convex versions of the operator systems and prove Stinespring theorem for local operator systems. A local operator C*-algebra is an example of a local operator system. Finally, we investigate the injectivity in both local operator space and local operator system senses, and prove locally conv...
Development of an incompressible navier-stokes solver with alternating cell direction implicit method on structured and unstructured quadrilateral grids
Baş, Onur; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2007)
In this research, the Alternating Cell Direction Implicit method is used in temporal discretisation of the incompressible Navier-Stokes equations and compared with the well known and widely used Point Gauss Seidel scheme on structured and quadrilateral unstructured meshes. A two dimensional, laminar and incompressible Navier-Stokes solver is developed for this purpose using the artificial compressibility formulation. The developed solver is used to obtain steady-state solutions with implicit time stepping m...
Citation Formats
H. Altundağ, “Inverse Sturm-Liouville Systems over the whole Real Line,” Ph.D. - Doctoral Program, Middle East Technical University, 2010.