@article{MTMT:34396234,
	title = {On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods},
	url = {https://m2.mtmt.hu/api/publication/34396234},
	author = {Matebie, Teshome Bayleyegn and Faragó, István and Havasi, Ágnes},
	doi = {10.1007/s10998-023-00557-y},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	unique-id = {34396234},
	issn = {0031-5303},
	abstract = {The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes h and h /2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from p to p+2 p + 2 , and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked.},
	year = {2024},
	eissn = {1588-2829},
	orcid-numbers = {Matebie, Teshome Bayleyegn/0000-0002-9277-4315; Faragó, István/0000-0002-4615-7615; Havasi, Ágnes/0000-0002-4125-4520}
}

@{MTMT:33835027,
	title = {On the Consistency and Convergence of Repeated Richardson Extrapolation},
	url = {https://m2.mtmt.hu/api/publication/33835027},
	author = {Matebie, Teshome Bayleyegn and Faragó, István and Havasi, Ágnes},
	booktitle = {Numerical Methods and Applications},
	doi = {10.1007/978-3-031-32412-3_5},
	unique-id = {33835027},
	year = {2023},
	pages = {48-58},
	orcid-numbers = {Matebie, Teshome Bayleyegn/0000-0002-9277-4315; Faragó, István/0000-0002-4615-7615; Havasi, Ágnes/0000-0002-4125-4520}
}

@{MTMT:33834370,
	title = {Mathematical Modelling of Nonlinear Heat Conduction with Relaxing Boundary Conditions},
	url = {https://m2.mtmt.hu/api/publication/33834370},
	author = {Filipov, Stefan M. and Faragó, István and Avdzhieva, Ana},
	booktitle = {Numerical Methods and Applications},
	doi = {10.1007/978-3-031-32412-3_13},
	unique-id = {33834370},
	year = {2023},
	pages = {146-158},
	orcid-numbers = {Filipov, Stefan M./0000-0002-2903-8315; Faragó, István/0000-0002-4615-7615; Avdzhieva, Ana/0000-0003-4973-3056}
}

@article{MTMT:33717531,
	title = {A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decoupling},
	url = {https://m2.mtmt.hu/api/publication/33717531},
	author = {Filipov, Stefan M. and Hristov, Jordan and Avdzhieva, Ana and Faragó, István},
	doi = {10.3390/axioms12040323},
	journal-iso = {AXIOMS},
	journal = {AXIOMS},
	volume = {12},
	unique-id = {33717531},
	abstract = {This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower temperature leaves the tank through another pipe. We propose a one-dimensional mathematical model that consists of a nonlinear PDE for the temperature along the solid body, coupled to a linear ODE for the temperature in the tank, the boundary and the initial conditions. All equations are converted into a dimensionless form reducing the input parameters to three dimensionless numbers and a dimensionless function. A steady-state analysis is performed. To solve the transient problem, a nontrivial numerical approach is proposed whereby the differential equations are first discretized in time. This reduces the problem to a sequence of nonlinear two-point boundary value problems (TPBVP) and a sequence of linear algebraic equations coupled to it. We show that knowing the temperature in the system at time level n − 1 allows us to decouple the TPBVP and the corresponding algebraic equation at time level n. Thus, starting from the initial conditions, the equations are decoupled and solved sequentially. The TPBVPs are solved by FDM with the Newtonian method.},
	keywords = {nonlinear; heat equation; finite difference method; coupled PDE-ODE system; TPBVP},
	year = {2023},
	eissn = {2075-1680},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@article{MTMT:33583456,
	title = {On the Consistency and Convergence of Classical Richardson Extrapolation as Applied to Explicit One-Step Methods},
	url = {https://m2.mtmt.hu/api/publication/33583456},
	author = {Matebie, Teshome Bayleyegn and Faragó, István and Havasi, Ágnes},
	doi = {10.3846/mma.2023.16283},
	journal-iso = {MATH MODEL ANAL},
	journal = {MATHEMATICAL MODELLING AND ANALYSIS},
	volume = {28},
	unique-id = {33583456},
	issn = {1392-6292},
	abstract = {The consistency of the classical Richardson extrapolation (CRE), a simple and robust computational device, is analysed for the case where the underlying method is an explicit one-step numerical method for ordinary differential equations with order of consistency one or two. It is shown in the classical framework that the CRE increases the order of consistency by one. The convergence of the method is proved by the assumption that the time-stepping operator of the base method has the Lipschitz property in its second argument.},
	year = {2023},
	eissn = {1648-3510},
	pages = {42-52},
	orcid-numbers = {Matebie, Teshome Bayleyegn/0000-0002-9277-4315; Faragó, István/0000-0002-4615-7615; Havasi, Ágnes/0000-0002-4125-4520}
}

@article{MTMT:33202585,
	title = {Some qualitative properties of the discrete models for malaria propagation},
	url = {https://m2.mtmt.hu/api/publication/33202585},
	author = {Faragó, István and Mosleh, Rahele},
	doi = {10.1016/j.amc.2022.127628},
	journal-iso = {APPL MATH COMPUT},
	journal = {APPLIED MATHEMATICS AND COMPUTATION},
	volume = {439},
	unique-id = {33202585},
	issn = {0096-3003},
	year = {2023},
	eissn = {1873-5649},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@inproceedings{MTMT:33300454,
	title = {Qualitatively Correct Numerical Methods for the Basic Ross–Macdonald Malaria Model},
	url = {https://m2.mtmt.hu/api/publication/33300454},
	author = {Faragó, István and Mincsovics, Miklós Emil and Mosleh, Rahele},
	booktitle = {Progress in Industrial Mathematics at ECMI 2021},
	doi = {10.1007/978-3-031-11818-0_11},
	unique-id = {33300454},
	year = {2022},
	pages = {75-81},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@inproceedings{MTMT:33300442,
	title = {Effectivity Analysis of Operator Splitting and the Average Method},
	url = {https://m2.mtmt.hu/api/publication/33300442},
	author = {Boda, Lívia and Faragó, István},
	booktitle = {Progress in Industrial Mathematics at ECMI 2021},
	doi = {10.1007/978-3-031-11818-0_6},
	unique-id = {33300442},
	year = {2022},
	pages = {39-45},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@{MTMT:33202900,
	title = {The Carleman Linearization Method for Boundary Value Problems},
	url = {https://m2.mtmt.hu/api/publication/33202900},
	author = {Svantnerné Sebestyén, Gabriella and Faragó, István},
	booktitle = {Advances in Mathematics Research},
	unique-id = {33202900},
	year = {2022},
	pages = {259-292},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@article{MTMT:32862432,
	title = {Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions},
	url = {https://m2.mtmt.hu/api/publication/32862432},
	author = {Takács, Bálint and Faragó, István and Horváth, Róbert and Repovš, Dušan},
	doi = {10.1515/cmam-2021-0208},
	journal-iso = {COMPUT METHODS APPL MATH},
	journal = {COMPUTATIONAL METHODS IN APPLIED MATHEMATICS},
	volume = {22},
	unique-id = {32862432},
	issn = {1609-4840},
	abstract = {In this article, a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We propose some numerical schemes and show that, by choosing the time step to be sufficiently small, the schemes preserve the qualitative properties of the original continuous model. Finally, some numerical experiments are presented that confirm the aforementioned theoretical results.},
	year = {2022},
	eissn = {1609-9389},
	pages = {713-728},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615; Repovš, Dušan/0000-0002-6643-1271}
}