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István Faragó

Bio: István Faragó is an academic researcher from Eötvös Loránd University. The author has contributed to research in topics: Richardson extrapolation & Boundary value problem. The author has an hindex of 21, co-authored 145 publications receiving 1521 citations. Previous affiliations of István Faragó include Budapest University of Technology and Economics & Hungarian Academy of Sciences.


Papers
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Journal ArticleDOI
01 May 2007
TL;DR: This paper suggests a new method which is based on the combination of the splitting time interval and the traditional iterative operator splitting, and analyses the local splitting error of the method.
Abstract: The operator-splitting methods are based on splitting of the complex problem into a sequence of simpler tasks. A useful method is the iterative splitting method which ensures a consistent approximation in each step. In our paper, we suggest a new method which is based on the combination of the splitting time interval and the traditional iterative operator splitting. We analyse the local splitting error of the method. Numerical examples are given in order to demonstrate the method.

97 citations

Journal ArticleDOI
TL;DR: The weighted sequential splittings are introduced and their local splitting error is analyzed and new results are presented for the case where the subproblems of the weighted splitting schemes are solved numerically.
Abstract: Operator splitting is a widely used procedure in the numerical solution of parabolicproblems. Several splitting methods have been constructed and used in the fields of applied mathematics. In this paper the weighted sequential splittings are introduced and their local splitting error is analyzed. New results are presented for the case where the subproblems of the weighted splitting schemes are solved numerically. The results are illustrated with test examples for ordinary differential systems.

93 citations

Book
01 Jan 2002
TL;DR: This paper presents an algorithmmic realisation of iterative methods based on pre-conditioning operators for iterative solution of non-LINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS.
Abstract: Contents: MOTIVATION -- Non-linear elliptic equations in model problems Linear algebraic systems Linear elliptic problems Non-linear algebraic systems and preconditioning. THEORETICAL BACKGROUND -- Non-linear equations in Hilbert space Solvability of non-linear elliptic problems. ITERATIVE SOLUTION OF NON-LINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS -- Iterative methods in Sobolev space Preconditioning strategies for discretise non-linear elliptic problems based on preconditioning operators Algorithmic realisation of iterative methods based on pre-conditioning operators Some numerical algorithms for non-linear elliptic problems in physics Appendix Index.

87 citations

Book
01 Jan 2008
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.
Abstract: The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. I. Dimov, I. Faragó, L. Vulkov (Eds.) Numerical Analysis and Its Applications

80 citations

Journal ArticleDOI
TL;DR: This paper analyses the connections between the different qualitative properties of numerical solutions of linear parabolic problems with Dirichlet-type boundary condition and shows that the nonnegativity preservation property is equivalent to the maximum-minimum principle and they imply the maximum norm contractivity.
Abstract: In this paper, we analyze the connections between the different qualitative properties of numerical solutions of linear parabolic problems with Dirichlet-type boundary condition. First we formulate the qualitative properties for the differential equations and shed light on their relations. Then we show how the well-known discretization schemes can be written in the form of a one-step iterative process. We give necessary and sufficient conditions of the main qualitative properties of these iterations. We apply the results to the finite difference and Galerkin finite element solutions of linear parabolic problems. In our main result we show that the nonnegativity preservation property is equivalent to the maximum-minimum principle and they imply the maximum norm contractivity. In one, two, and three dimensions, we list sufficient a priori conditions that ensure the required qualitative properties. Finally, we demonstrate the above results on numerical examples.

64 citations


Cited by
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01 Apr 2003
TL;DR: The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it as mentioned in this paper, and also presents new ideas and alternative interpretations which further explain the success of the EnkF.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

2,975 citations

Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

2,446 citations

Journal ArticleDOI
Tamar Frankel1
TL;DR: The Essay concludes that practitioners theorize, and theorists practice, use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ.
Abstract: Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

2,077 citations

01 Mar 1987
TL;DR: The variable-order Adams method (SIVA/DIVA) package as discussed by the authors is a collection of subroutines for solution of non-stiff ODEs.
Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

1,955 citations