TY - JOUR AU - Matebie, Teshome Bayleyegn AU - Faragó, István AU - Havasi, Ágnes TI - On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods JF - PERIODICA MATHEMATICA HUNGARICA J2 - PERIOD MATH HUNG PY - 2024 SN - 0031-5303 DO - 10.1007/s10998-023-00557-y UR - https://m2.mtmt.hu/api/publication/34396234 ID - 34396234 N1 - Export Date: 7 December 2023 Correspondence Address: Havasi, Á.; HUN-REN-ELTE Numerical Analysis and Large Networks Research Group, Pázmány Péter s. 1/C, Hungary; email: agnes.havasi@ttk.elte.hu AB - 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. LA - English DB - MTMT ER - TY - CHAP AU - Matebie, Teshome Bayleyegn AU - Faragó, István AU - Havasi, Ágnes ED - Nikolov, Geno ED - Georgiev, Krassimir ED - Datcheva, Maria ED - Georgiev, Ivan TI - On the Consistency and Convergence of Repeated Richardson Extrapolation T2 - Numerical Methods and Applications PB - Springer Nature Switzerland AG CY - Cham SN - 9783031324123 T3 - Lecture Notes in Computer Science, ISSN 0302-9743 ; 13858. PY - 2023 SP - 48 EP - 58 PG - 11 DO - 10.1007/978-3-031-32412-3_5 UR - https://m2.mtmt.hu/api/publication/33835027 ID - 33835027 N1 - Export Date: 22 June 2023 Correspondence Address: Faragó, I.; ELTE Eötvös Loránd University, Pázmány Péter s. 1/C, Hungary; email: faragois@gmail.com LA - English DB - MTMT ER - TY - CHAP AU - Filipov, Stefan M. AU - Faragó, István AU - Avdzhieva, Ana ED - Nikolov, Geno ED - Georgiev, Krassimir ED - Datcheva, Maria ED - Georgiev, Ivan TI - Mathematical Modelling of Nonlinear Heat Conduction with Relaxing Boundary Conditions T2 - Numerical Methods and Applications PB - Springer Nature Switzerland AG CY - Cham SN - 9783031324123 T3 - Lecture Notes in Computer Science, ISSN 0302-9743 ; 13858. PY - 2023 SP - 146 EP - 158 PG - 13 DO - 10.1007/978-3-031-32412-3_13 UR - https://m2.mtmt.hu/api/publication/33834370 ID - 33834370 N1 - Cited By :1 Export Date: 22 February 2024 Correspondence Address: Filipov, S.M.; Department of Computer Science, Bulgaria; email: sfilipov@uctm.edu LA - English DB - MTMT ER - TY - JOUR AU - Filipov, Stefan M. AU - Hristov, Jordan AU - Avdzhieva, Ana AU - Faragó, István TI - 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 JF - AXIOMS J2 - AXIOMS VL - 12 PY - 2023 IS - 4 SN - 2075-1680 DO - 10.3390/axioms12040323 UR - https://m2.mtmt.hu/api/publication/33717531 ID - 33717531 N1 - Department of Computer Science, Faculty of Chemical and System Engineering, University of Chemical Technology and Metallurgy, Sofia, 1756, Bulgaria Department of Chemical Engineering, Faculty of Chemical and System Engineering, University of Chemical Technology and Metallurgy, Sofia, 1756, Bulgaria Department of Numerical Methods and Algorithms, Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski, Sofia, 1164, Bulgaria Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, 1111, Hungary ELKH-ELTE NumNet Research Group, Budapest, 1117, Hungary Export Date: 5 May 2023 Correspondence Address: Faragó, I.; Department of Differential Equations, Hungary; email: faragois@gmail.com AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Matebie, Teshome Bayleyegn AU - Faragó, István AU - Havasi, Ágnes TI - On the Consistency and Convergence of Classical Richardson Extrapolation as Applied to Explicit One-Step Methods JF - MATHEMATICAL MODELLING AND ANALYSIS J2 - MATH MODEL ANAL VL - 28 PY - 2023 IS - 1 SP - 42 EP - 52 PG - 11 SN - 1392-6292 DO - 10.3846/mma.2023.16283 UR - https://m2.mtmt.hu/api/publication/33583456 ID - 33583456 N1 - Correspondence Address: Havasi, Á.; Applied Analysis and Computational Mathematics, Pázmány Péter s. 1/C, Hungary; email: agnes.havasi@ttk.elte.hu AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Faragó, István AU - Mosleh, Rahele TI - Some qualitative properties of the discrete models for malaria propagation JF - APPLIED MATHEMATICS AND COMPUTATION J2 - APPL MATH COMPUT VL - 439 PY - 2023 PG - 18 SN - 0096-3003 DO - 10.1016/j.amc.2022.127628 UR - https://m2.mtmt.hu/api/publication/33202585 ID - 33202585 N1 - Department of Differential Equations at Budapest University of Technology and Economics, Hungary Department of Applied Analysis and Computational Mathematics at Eötvös Loránd University, Hungary Numerical Analysis and Large Networks Research Group at ELKH-ELTE, Hungary CODEN: AMHCB Correspondence Address: Mosleh, R.; Department of Differential Equations at Budapest University of Technology and EconomicsHungary; email: rmosleh028@gmail.com LA - English DB - MTMT ER - TY - CHAP AU - Faragó, István AU - Mincsovics, Miklós Emil AU - Mosleh, Rahele ED - Günther, Michael ED - Ehrhardt, Matthias TI - Qualitatively Correct Numerical Methods for the Basic Ross–Macdonald Malaria Model T2 - Progress in Industrial Mathematics at ECMI 2021 PB - Springer Netherlands CY - Cham SN - 9783031118180 T3 - Mathematics in industry, ISSN 1612-3956 ; 39. PY - 2022 SP - 75 EP - 81 PG - 7 DO - 10.1007/978-3-031-11818-0_11 UR - https://m2.mtmt.hu/api/publication/33300454 ID - 33300454 N1 - Department of Differential Equations, Budapest University of Technology and Economics, Budapest, Hungary Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Budapest, Hungary Large Networks Research Group, ELKH, Budapest, Hungary Budapest University of Technology and Economics, Budapest, Hungary Correspondence Address: Mosleh, R.; Budapest University of Technology and EconomicsHungary; email: rmosleh@math.bme.hu LA - English DB - MTMT ER - TY - CHAP AU - Boda, Lívia AU - Faragó, István ED - Günther, Michael ED - Ehrhardt, Matthias TI - Effectivity Analysis of Operator Splitting and the Average Method T2 - Progress in Industrial Mathematics at ECMI 2021 PB - Springer Netherlands CY - Cham SN - 9783031118180 T3 - Mathematics in industry, ISSN 1612-3956 ; 39. PY - 2022 SP - 39 EP - 45 PG - 7 DO - 10.1007/978-3-031-11818-0_6 UR - https://m2.mtmt.hu/api/publication/33300442 ID - 33300442 N1 - Funding Agency and Grant Number: National Research, Development and Innovation Office - NKFIH [K137699] Funding text: This research has been supported by the National Research, Development and Innovation Office - NKFIH, grant no. K137699. LA - English DB - MTMT ER - TY - CHAP AU - Svantnerné Sebestyén, Gabriella AU - Faragó, István ED - Albert, R. Baswell TI - The Carleman Linearization Method for Boundary Value Problems T2 - Advances in Mathematics Research PB - Nova Science Publishers CY - New York, New York SN - 9798886973327 T3 - Advances in Mathematics Research ; 32. PY - 2022 SP - 259 EP - 292 PG - 34 UR - https://m2.mtmt.hu/api/publication/33202900 ID - 33202900 LA - English DB - MTMT ER - TY - JOUR AU - Takács, Bálint AU - Faragó, István AU - Horváth, Róbert AU - Repovš, Dušan TI - Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions JF - COMPUTATIONAL METHODS IN APPLIED MATHEMATICS J2 - COMPUT METHODS APPL MATH VL - 22 PY - 2022 IS - 3 SP - 713 EP - 728 PG - 16 SN - 1609-4840 DO - 10.1515/cmam-2021-0208 UR - https://m2.mtmt.hu/api/publication/32862432 ID - 32862432 N1 - Funding Agency and Grant Number: NRDI Fund (TKP2020 NC) under Ministry for Innovation and Technology; Hungarian Ministry of Human Capacities OTKA grant [SNN125119]; Hungarian Ministry of Human Capacities [TKP2020-IKA-05]; Slovenian Research Agency [P1-0292, N1-0114, N1-0083, N1-0064, J1-8131] Funding text: The research by the authors B. M. Takacs, I. Farago and R. Horvath reported in this paper and carried out at BME has been supported by the NRDI Fund (TKP2020 NC, Grant No. BME-NC) based on the charter of bolster issued by the NRDI Office under the auspices of the Ministry for Innovation and Technology, and the Hungarian Ministry of Human Capacities OTKA grant SNN125119. The work of the author I. Farago was completed in the ELTE Institutional Excellence Program (TKP2020-IKA-05) financed by the Hungarian Ministry of Human Capacities. The research of the author D. Repovs reported in this paper was supported by the Slovenian Research Agency grants P1-0292, N1-0114, N1-0083, N1-0064 and J1-8131. AB - 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. LA - English DB - MTMT ER -