Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Evolution operator approach for solving linear ordinary differential equations and computation of EXP (A)
Download
014603.pdf
Date
1991
Author
Azzam, Abdelnasser
Metadata
Show full item record
Item Usage Stats
44
views
0
downloads
Cite This
An Evolution Operator Approach which were developed to solve nonlinear O.D.E. systems, X=f(x), X(0)=£, is discussed for the linear systems X=AX where A is nxn symmetric matrix. In this approach, each component of the solution vector is represented as an action of evolution operator, exp(itL), on xj and then approximated by method of Moment using [N+1,N] Pade’ approximation. In applications, the most important part of this method is the computation of dynamical and spectral coefficients [6]. The recursive formulation of the dynamical coefficients are used to achieve the analytic formulation of spectral coefficients for the case N=l. The exponential matrix, eA, for symmetric matrix A, is computed approximately using the numerical solution of the initial value problem with the initial conditions X(0) = e , j=l,2, ...,n. Also some modifications are applied to improve die numerical results.
Subject Keywords
Linear Differential Equations
,
Symmetric Matrix
,
Evolution Operator Approach
,
Dynamical Coefficients
,
Spectral Coefficients
,
Exponential Matrix
URI
https://hdl.handle.net/11511/3281
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Vester's Sensitivity Model for Genetic Networks with Time-Discrete Dynamics
Moreno, Liana Amaya; DEFTERLİ, ÖZLEM; Fuegenschuh, Armin; Weber, Gerhard Wilhelm (2014-07-03)
We propose a new method to explore the characteristics of genetic networks whose dynamics are described by a linear discrete dynamical model x(t+1) = Ax(t). The gene expression data x(t) is given for various time points and the matrix A of interactions among the genes is unknown. First we formulate and solve a parameter estimation problem by linear programming in order to obtain the entries of the matrix A. We then use ideas from Vester's Sensitivity Model, more precisely, the Impact Matrix, and the determi...
Modified iterative methods for linear systems of equations
Karasözen, Bülent (1998-01-01)
An extension of the modified Jacobi and Gauss-Seidel methods for systems of linear equations has been introduced. The convergence properties of the proposed methods have been analyzed and compared with the classical and modified methods. The numerical results obtained for some linear systems show that the extended modified methods are superior to other modified iterative methods.
Stability in cellular neural networks with a piecewise constant argument
Akhmet, Marat; Yılmaz, Elanur (2010-03-01)
In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.
Transformation Electromagnetics Based Analysis of Waveguides With Random Rough or Periodic Grooved Surfaces
Ozgun, Ozlem; Kuzuoğlu, Mustafa (Institute of Electrical and Electronics Engineers (IEEE), 2013-02-01)
A computational model is introduced which employs transformation-based media to increase the computational performance of finite methods (such as finite element or finite difference methods) for analyzing waveguides with grooves or rough surfaces. Random behavior of the roughness is taken into account by utilizing the Monte Carlo technique, which is based on a set of random rough surfaces generated from Gaussian distribution. The main objective of the proposed approach is to create a single mesh, and to ana...
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes
İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013)
Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. Azzam, “Evolution operator approach for solving linear ordinary differential equations and computation of EXP (A),” Middle East Technical University, 1991.