Pseudospectral methods for differential equations : application to the Schrödinger type eigenvalue problems

Download

index.pdf

Date

2003

Author

Alıcı, Haydar

Metadata

Show full item record

Item Usage Stats

209
views

0
downloads

In this thesis, a survey on pseudospectral methods for differential equations is presented. Properties of the classical orthogonal polynomials required in this context are reviewed. Differentiation matrices corresponding to Jacobi, Laguerre,and Hermite cases are constructed. A fairly detailed investigation is made for the Hermite spectral methods, which is applied to the Schrödinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then introduced to deduce the effciency of the method.

Subject Keywords

Spectral theory (Mathematics), Schrodinger equation, Pseudospectral (collocation) methods, Differentiation matrices, Her mite spectral methods, Schrödinger equation, Quantum mechanical potentials with single and multiminima

URI

http://etd.lib.metu.edu.tr/upload/1086198/index.pdf
https://hdl.handle.net/11511/13891

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Probabilistic Slope Stability Analyses Using Limit Equilibrium and Finite Element Methods Akbas, Burak; Huvaj Sarıhan, Nejan (2015-10-16) This paper compares the results of different probabilistic approaches and emphasizes the necessity of probabilistic analyses in slope stability studies. To do that, Limit Equilibrium Method (LEM) and Finite Element Method (FEM) are utilized and their outputs are compared in terms of probability of failure (PF), reliability index (RI), factor of safety (FS) and the failure surface. Lastly, concept of Random Finite Element Method (RFEM) is studied and effects of spatial correlation distance are investigated.
Periodic solutions and stability of differential equations with piecewise constant argument of generalized type Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009) In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...
Energy bounds for some nonstandard problems in partial differential equations Özer, Özge; Çelebi, Okay; Department of Mathematics (2005) This thesis is a survey of the studies of Ames,Payne and Schaefer about the partial differential equations with nonstandard auxiliary conditions; this is where the values of the solution are prescribed as a combination of initial time t=0 and at a later time t=T. The first chaper is introductory and contains some historical background of the problem,basic definitions and theorems.In Chapter 2 energy bounds and pointwise bounds for the solutions of the nonstandard hyperbolic problems have been investigated a...
Integral manifolds of differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-01-15) In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG). The existence of global integral manifolds of the quasilinear EPCAG is established when the associated linear homogeneous system has an exponential dichotomy. The smoothness of the manifolds is investigated. The existence of bounded and periodic solutions is considered. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Ap...
Oscillation of integro-dynamic equations on time scales Grace, Said R.; Graef, John R.; Zafer, Ağacık (2013-04-01) In this paper, the authors initiate the study of oscillation theory for integro-dynamic equations on time-scales. They present some new sufficient conditions guaranteeing that the oscillatory character of the forcing term is inherited by the solutions.

Citation Formats

H. Alıcı, “Pseudospectral methods for differential equations : application to the Schrödinger type eigenvalue problems,” M.S. - Master of Science, Middle East Technical University, 2003.