Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
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
An error analysis of iterated defect correction methods for linear differential-algebraic equations
Date
1996-01-01
Author
Karasözen, Bülent
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
218
views
0
downloads
Cite This
Asymptotic expansions of the global error of iterated defect correction (IDeC) techniques based on the implicit Euler method for linear differential-algebraic equations (dae's) of arbitrary index are analyzed. The dependence of the maximum attainable convergence order on the degree of the interpolating polynomial, number of defect correction steps, and on the index of the differential-algebraic system is given. The efficiency of IDeC method and extrapolation is compared on the basis of numerical experiments and comparing computational cost for both methods. Linear time-varying differential-algebraic equations are investigated by presenting numerical results and extending theoretical results for constant coefficient to these problems.
Subject Keywords
differential-algebraic equations
,
implicit Euler method
,
iterated defect correction methods
,
extrapolation
URI
https://hdl.handle.net/11511/30971
Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
DOI
https://doi.org/10.1080/00207169608804480
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012)
Bayin, Selcuk S. (2012-08-01)
Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations
ALTINTAN, DERYA; Uğur, Ömür (2011-11-01)
In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses restricted variations only for nonlinear terms by generalising the Lagrange multipliers. Consequently, this allows us t...
An anticipatory extension of Malthusian model
Akhmet, Marat; Öktem, Hüseyin Avni (2005-08-13)
In this paper, on the base of a new variable - deviation of population from an average value, we propose a new extension of the Malthusian model (see equations (10), (15) and (20)) using differential equations with piecewise constant argument which can be retarded as well as advanced. We study existence of periodic solutions and stability of the equations by method of reduction to discrete equations [4]. Equations (15) and (20) with advanced argument are systems with strong anticipation [6, 7]. Moreover, we...
A ROBUST ITERATIVE SCHEME FOR SYMMETRIC INDEFINITE SYSTEMS
Manguoğlu, Murat (Society for Industrial & Applied Mathematics (SIAM), 2019-01-01)
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with a relatively small number of negative eigenvalues. The proposed scheme consists of an outer minimum residual (MINRES) iteration, preconditioned by an inner conjugate gradient (CG) iteration in which CG can be further preconditioned. The robustness of the proposed scheme is illustrated by solving indefinite linear systems that arise in t...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
B. Karasözen, “An error analysis of iterated defect correction methods for linear differential-algebraic equations,”
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
, pp. 121–137, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30971.