István Faragó | Eötvös Loránd University (original) (raw)

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Papers by István Faragó

Research paper thumbnail of Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation

Advection equations appear often in large-scale mathematical models arising in many fields of sci... more Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.

Research paper thumbnail of On the maximum norm contractivity of the Crank-Nicholson method

Research paper thumbnail of Convergence of semidiscrete Galerkin approximations for generalized nonlinear parabolic problems

Research paper thumbnail of Solution of parabolic problems with different discretizations

Research paper thumbnail of Properties of two additive splitting procedures

Two additive splitting procedures are defined and studied in this paper. It is shown that these s... more Two additive splitting procedures are defined and studied in this paper. It is shown that these splitting procedures have good stability properties. Some other splitting procedures, which are traditionally used in mathematical models used in many scientific and engineering fields, are sketched. Some conclusions, which are related to the comparison of the additive splitting procedures with the other splitting procedures, are drawn.

Research paper thumbnail of Nonnegativity of the difference schemes

Research paper thumbnail of Convergence of semidiscrete Galerkin approximations for parabolic equations with signdeterminated nonlinearity

Research paper thumbnail of Solution of nonlinear partial differential equations of parabolic type with boundary condition of Neumann type in the non-Lipschitzian case

Research paper thumbnail of Analysis of mathematical models of kinetic reactions and their numerical solution with the Galerkin method

Research paper thumbnail of Finite element discretization of linear and nonlinear parabolic type differential equations

Research paper thumbnail of An A-stable three-level method for the Galerkin solution of quasilinear parabolic problems

Research paper thumbnail of Special issue: Selected papers of the 3rd joint conference on mathematics and computer science, Visegrád, Hungary, June 6–12, 1999

Research paper thumbnail of Stochastic regular splitting and its application to the iterative methods

Research paper thumbnail of Special issue: FDM: TA’2010. Papers based on the presentations at the 5th international conference on finite difference methods: Theory and applications, Lozenetz, Bulgaria, August 26–29, 2010

Research paper thumbnail of Stability of patterns and of constant steady states for a cross-diffusion system

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of On some qualitatively adequate discrete space–time models of epidemic propagation

Journal of Computational and Applied Mathematics, 2015

ABSTRACT Most of the models of epidemic propagations do not take into account the spatial distrib... more ABSTRACT Most of the models of epidemic propagations do not take into account the spatial distribution of the individuals. They give only the temporal change of the number of the infected, susceptible and recovered patients. In this paper we give some spatial discrete one-step iteration models for disease propagation and give conditions that guarantee some basic qualitative properties of the original process to the discrete models. Since the discrete models can be considered as the finite difference discretizations of continuous models of disease propagation given in the form of systems of partial differential equations, we can deduce conditions for the mesh size and the time step. Some of the results are demonstrated on numerical tests.

Research paper thumbnail of Proper Weak Regular Splitting for M-Matrices

Lecture Notes in Computer Science, 2001

ABSTRACT

Research paper thumbnail of Qualitative Analysis of the Crank-Nicolson Method for the Heat Conduction Equation

Lecture Notes in Computer Science, 2009

ABSTRACT The preservation of the basic qualitative properties – besides the convergence – is a ba... more ABSTRACT The preservation of the basic qualitative properties – besides the convergence – is a basic requirement in the numerical solution process. For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. In this paper we formulate the discrete qualitative properties and we also analyze the condition w.r.t. the discretization step sizes under which the different qualitative properties are preserved. We give exact conditions for the discretization of the one-dimensional heat conduction problem under which the basic qualitative properties are preserved.

Research paper thumbnail of Note on the Convergence of the Implicit Euler Method

Lecture Notes in Computer Science, 2013

Research paper thumbnail of Numerical stability for nonlinear evolution equations

Computers & Mathematics with Applications, 2015

The paper deals with discretisation methods for nonlinear operator equations written as abstract ... more The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for the implicit Euler method. Motivated by the rational approximation methods for linear semigroups, we propose a more general time discretisation method and prove its Nstability as well.

Research paper thumbnail of Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation

Advection equations appear often in large-scale mathematical models arising in many fields of sci... more Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.

Research paper thumbnail of On the maximum norm contractivity of the Crank-Nicholson method

Research paper thumbnail of Convergence of semidiscrete Galerkin approximations for generalized nonlinear parabolic problems

Research paper thumbnail of Solution of parabolic problems with different discretizations

Research paper thumbnail of Properties of two additive splitting procedures

Two additive splitting procedures are defined and studied in this paper. It is shown that these s... more Two additive splitting procedures are defined and studied in this paper. It is shown that these splitting procedures have good stability properties. Some other splitting procedures, which are traditionally used in mathematical models used in many scientific and engineering fields, are sketched. Some conclusions, which are related to the comparison of the additive splitting procedures with the other splitting procedures, are drawn.

Research paper thumbnail of Nonnegativity of the difference schemes

Research paper thumbnail of Convergence of semidiscrete Galerkin approximations for parabolic equations with signdeterminated nonlinearity

Research paper thumbnail of Solution of nonlinear partial differential equations of parabolic type with boundary condition of Neumann type in the non-Lipschitzian case

Research paper thumbnail of Analysis of mathematical models of kinetic reactions and their numerical solution with the Galerkin method

Research paper thumbnail of Finite element discretization of linear and nonlinear parabolic type differential equations

Research paper thumbnail of An A-stable three-level method for the Galerkin solution of quasilinear parabolic problems

Research paper thumbnail of Special issue: Selected papers of the 3rd joint conference on mathematics and computer science, Visegrád, Hungary, June 6–12, 1999

Research paper thumbnail of Stochastic regular splitting and its application to the iterative methods

Research paper thumbnail of Special issue: FDM: TA’2010. Papers based on the presentations at the 5th international conference on finite difference methods: Theory and applications, Lozenetz, Bulgaria, August 26–29, 2010

Research paper thumbnail of Stability of patterns and of constant steady states for a cross-diffusion system

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of On some qualitatively adequate discrete space–time models of epidemic propagation

Journal of Computational and Applied Mathematics, 2015

ABSTRACT Most of the models of epidemic propagations do not take into account the spatial distrib... more ABSTRACT Most of the models of epidemic propagations do not take into account the spatial distribution of the individuals. They give only the temporal change of the number of the infected, susceptible and recovered patients. In this paper we give some spatial discrete one-step iteration models for disease propagation and give conditions that guarantee some basic qualitative properties of the original process to the discrete models. Since the discrete models can be considered as the finite difference discretizations of continuous models of disease propagation given in the form of systems of partial differential equations, we can deduce conditions for the mesh size and the time step. Some of the results are demonstrated on numerical tests.

Research paper thumbnail of Proper Weak Regular Splitting for M-Matrices

Lecture Notes in Computer Science, 2001

ABSTRACT

Research paper thumbnail of Qualitative Analysis of the Crank-Nicolson Method for the Heat Conduction Equation

Lecture Notes in Computer Science, 2009

ABSTRACT The preservation of the basic qualitative properties – besides the convergence – is a ba... more ABSTRACT The preservation of the basic qualitative properties – besides the convergence – is a basic requirement in the numerical solution process. For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. In this paper we formulate the discrete qualitative properties and we also analyze the condition w.r.t. the discretization step sizes under which the different qualitative properties are preserved. We give exact conditions for the discretization of the one-dimensional heat conduction problem under which the basic qualitative properties are preserved.

Research paper thumbnail of Note on the Convergence of the Implicit Euler Method

Lecture Notes in Computer Science, 2013

Research paper thumbnail of Numerical stability for nonlinear evolution equations

Computers & Mathematics with Applications, 2015

The paper deals with discretisation methods for nonlinear operator equations written as abstract ... more The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for the implicit Euler method. Motivated by the rational approximation methods for linear semigroups, we propose a more general time discretisation method and prove its Nstability as well.

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