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

Download
2003
Alıcı, Haydar
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.

Suggestions

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...
Asymptotic integration of impulsive differential equations
Doğru Akgöl, Sibel; Ağacık, Zafer; Özbekler, Abdullah; Department of Mathematics (2017)
The main objective of this thesis is to investigate asymptotic properties of the solutions of differential equations under impulse effect, and in this way to fulfill the gap in the literature about asymptotic integration of impulsive differential equations. In this process our main instruments are fixed point theorems; lemmas on compactness; principal and nonprincipal solutions of impulsive differential equations and Cauchy function for impulsive differential equations. The thesis consists of five chapters....
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...
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.