Edit Profile Arenas, Abraham J. Compute Distance To: Compute Author ID: arenas.abraham-j Published as: Arenas, A.; Arenas, Abraham; Arenas, Abraham J. Documents Indexed: 43 Publications since 1987 all top 5 Co-Authors 0 single-authored 21 González-Parra, Gilberto C. 8 Jódar Sanchez, Lucas Antonio 6 Chen-Charpentier, Benito M. 6 Villanueva, Rafael-Jacinto 3 Acedo, Luis 2 Aranda, Diego F. 2 González, Gilberto C. 1 Caraballo, Blas Melendez 1 Cortés López, Juan Carlos 1 Díaz-Rodríguez, Miguel 1 Guerrero, Francisco 1 Moraño, José Antonio 1 Santonja, Francisco-José 1 Villanueva Micó, Rafael J. all top 5 Serials 4 Computers & Mathematics with Applications 4 Mathematical and Computer Modelling 3 Mathematics and Computers in Simulation 2 Applied Mathematics and Computation 2 Computational and Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 Chaos, Solitons and Fractals 1 Theoretical Population Biology 1 Numerical Algorithms 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Biological Systems 1 Nonlinear Analysis. Real World Applications 1 Journal of Applied Mathematics 1 International Journal for Numerical Methods in Biomedical Engineering all top 5 Fields 19 Biology and other natural sciences (92-XX) 17 Numerical analysis (65-XX) 12 Ordinary differential equations (34-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 30 Publications have been cited 230 times in 153 Documents Cited by ▼ Year ▼ Nonstandard numerical methods for a mathematical model for influenza disease. Zbl 1151.92018Jódar, Lucas; Villanueva, Rafael J.; Arenas, Abraham J.; González, Gilberto C. 31 2008 Non-standard numerical method for a mathematical model of RSV epidemiological transmission. Zbl 1155.92337Arenas, Abraham J.; Moraño, José Antonio; Cortés, Juan Carlos 22 2008 A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1). Zbl 1300.92099González-Parra, Gilberto; Arenas, Abraham J.; Chen-Charpentier, Benito M. 19 2014 A nonstandard numerical scheme of predictor-corrector type for epidemic models. Zbl 1198.65116Arenas, Abraham J.; González-Parra, Gilberto; Chen-Charpentier, Benito M. 16 2010 Modeling the spread of seasonal epidemiological diseases: Theory and applications. Zbl 1145.92336Jódar, L.; Villanueva, R. J.; Arenas, A. 16 2008 Polynomial chaos for random fractional order differential equations. Zbl 1354.34017González-Parra, Gilberto; Chen-Charpentier, Benito; Arenas, Abraham J. 11 2014 Combination of nonstandard schemes and Richardson’s extrapolation to improve the numerical solution of population models. Zbl 1205.65015González-Parra, Gilberto; Arenas, Abraham J.; Chen-Charpentier, Benito M. 11 2010 A nonstandard dynamically consistent numerical scheme applied to obesity dynamics. Zbl 1157.92028Villanueva, Rafael J.; Arenas, Abraham J.; González-Parra, Gilberto 11 2008 Piecewise finite series solutions of seasonal diseases models using multistage Adomian method. Zbl 1221.65201González-Parra, Gilberto; Arenas, Abraham J.; Jódar, Lucas 10 2009 Existence of periodic solutions in a model of respiratory syncytial virus RSV. Zbl 1137.92318Arenas, Abraham J.; González, Gilberto; Jódar, Lucas 10 2008 On the short-time dynamics of networks of Hebbian coupled oscillators. Zbl 0937.92501Pérez Vicente, C. J.; Arenas, A.; Bonilla, L. L. 8 1996 A nonstandard finite difference scheme for a nonlinear Black-Scholes equation. Zbl 1305.91238Arenas, Abraham J.; González-Parra, Gilberto; Caraballo, Blas Melendez 7 2013 An exact global solution for the classical SIRS epidemic model. Zbl 1196.34058Acedo, L.; González-Parra, Gilberto; Arenas, Abraham J. 7 2010 Dynamics of a model of toxoplasmosis disease in human and cat populations. Zbl 1186.34063González-Parra, Gilberto C.; Arenas, Abraham J.; Aranda, Diego F.; Villanueva, Rafael J.; Jódar, Lucas 7 2009 Piecewise finite series solution of nonlinear initial value differential problem. Zbl 1166.65350Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas; Villanueva, Rafael-J. 7 2009 Modeling toxoplasmosis spread in cat populations under vaccination. Zbl 1403.92115Arenas, Abraham J.; González-Parra, Gilberto; Villanueva Micó, Rafael-J. 6 2010 Mathematical modeling of toxoplasmosis disease in varying size populations. Zbl 1155.92336Aranda, Diego F.; Villanueva, Rafael J.; Arenas, Abraham J.; González-Parra, Gilberto C. 5 2008 Randomness in a mathematical model for the transmission of respiratory syncytial virus (RSV). Zbl 1184.92027Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas 3 2010 Periodic solutions of nonautonomous differential systems modeling obesity population. Zbl 1198.34063Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas 3 2009 Dynamical analysis of the transmission of seasonal diseases using the differential transformation method. Zbl 1185.37177Arenas, Abraham J.; González-Parra, Gilberto; Chen-Charpentier, Benito M. 3 2009 A nonstandard finite difference numerical scheme applied to a mathematical model of the prevalence of smoking in Spain: a case study. Zbl 1329.91108Guerrero, Francisco; González-Parra, Gilberto; Arenas, Abraham J. 2 2014 Accuracy of analytical-numerical solutions of the Michaelis-Menten equation. Zbl 1229.92042Gonzalez-Parra, Gilberto; Acedo, Luis; Arenas, Abraham 2 2011 On the traces of Hecke operators. Zbl 1030.11020Arenas, A. 2 2003 The simulation and interpretation of free turbulence with a cognitive neural system. Zbl 1184.76181Giralt, Francesc; Arenas, A.; Ferre-Giné, J.; Rallo, R.; Kopp, G. A. 2 2000 On some equivalences of positive definite binary quadratic forms. Zbl 0691.10012Arenas, A. 2 1989 An arithmetic problem on the sums of three squares. Zbl 0663.10050Arenas, A. 2 1988 Arithmetic behaviour of the sums of three squares. Zbl 0623.10035Arenas, A.; Bayer, P. 2 1987 Nonstandard numerical schemes for modeling a 2-DOF serial robot with rotational spring-damper-actuators. Zbl 1358.70002Díaz-Rodríguez, Miguel; González-Parra, Gilberto; Arenas, Abraham J. 1 2011 Rational equivalence of primitive integral binary quadratic forms. Zbl 0738.11035Arenas, A. 1 1991 Quantitative aspects of the representations of integers by quadratic forms. Zbl 0695.10018Arenas, A. 1 1989 A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1). Zbl 1300.92099González-Parra, Gilberto; Arenas, Abraham J.; Chen-Charpentier, Benito M. 19 2014 Polynomial chaos for random fractional order differential equations. Zbl 1354.34017González-Parra, Gilberto; Chen-Charpentier, Benito; Arenas, Abraham J. 11 2014 A nonstandard finite difference numerical scheme applied to a mathematical model of the prevalence of smoking in Spain: a case study. Zbl 1329.91108Guerrero, Francisco; González-Parra, Gilberto; Arenas, Abraham J. 2 2014 A nonstandard finite difference scheme for a nonlinear Black-Scholes equation. Zbl 1305.91238Arenas, Abraham J.; González-Parra, Gilberto; Caraballo, Blas Melendez 7 2013 Accuracy of analytical-numerical solutions of the Michaelis-Menten equation. Zbl 1229.92042Gonzalez-Parra, Gilberto; Acedo, Luis; Arenas, Abraham 2 2011 Nonstandard numerical schemes for modeling a 2-DOF serial robot with rotational spring-damper-actuators. Zbl 1358.70002Díaz-Rodríguez, Miguel; González-Parra, Gilberto; Arenas, Abraham J. 1 2011 A nonstandard numerical scheme of predictor-corrector type for epidemic models. Zbl 1198.65116Arenas, Abraham J.; González-Parra, Gilberto; Chen-Charpentier, Benito M. 16 2010 Combination of nonstandard schemes and Richardson’s extrapolation to improve the numerical solution of population models. Zbl 1205.65015González-Parra, Gilberto; Arenas, Abraham J.; Chen-Charpentier, Benito M. 11 2010 An exact global solution for the classical SIRS epidemic model. Zbl 1196.34058Acedo, L.; González-Parra, Gilberto; Arenas, Abraham J. 7 2010 Modeling toxoplasmosis spread in cat populations under vaccination. Zbl 1403.92115Arenas, Abraham J.; González-Parra, Gilberto; Villanueva Micó, Rafael-J. 6 2010 Randomness in a mathematical model for the transmission of respiratory syncytial virus (RSV). Zbl 1184.92027Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas 3 2010 Piecewise finite series solutions of seasonal diseases models using multistage Adomian method. Zbl 1221.65201González-Parra, Gilberto; Arenas, Abraham J.; Jódar, Lucas 10 2009 Dynamics of a model of toxoplasmosis disease in human and cat populations. Zbl 1186.34063González-Parra, Gilberto C.; Arenas, Abraham J.; Aranda, Diego F.; Villanueva, Rafael J.; Jódar, Lucas 7 2009 Piecewise finite series solution of nonlinear initial value differential problem. Zbl 1166.65350Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas; Villanueva, Rafael-J. 7 2009 Periodic solutions of nonautonomous differential systems modeling obesity population. Zbl 1198.34063Arenas, Abraham J.; González-Parra, Gilberto; Jódar, Lucas 3 2009 Dynamical analysis of the transmission of seasonal diseases using the differential transformation method. Zbl 1185.37177Arenas, Abraham J.; González-Parra, Gilberto; Chen-Charpentier, Benito M. 3 2009 Nonstandard numerical methods for a mathematical model for influenza disease. Zbl 1151.92018Jódar, Lucas; Villanueva, Rafael J.; Arenas, Abraham J.; González, Gilberto C. 31 2008 Non-standard numerical method for a mathematical model of RSV epidemiological transmission. Zbl 1155.92337Arenas, Abraham J.; Moraño, José Antonio; Cortés, Juan Carlos 22 2008 Modeling the spread of seasonal epidemiological diseases: Theory and applications. Zbl 1145.92336Jódar, L.; Villanueva, R. J.; Arenas, A. 16 2008 A nonstandard dynamically consistent numerical scheme applied to obesity dynamics. Zbl 1157.92028Villanueva, Rafael J.; Arenas, Abraham J.; González-Parra, Gilberto 11 2008 Existence of periodic solutions in a model of respiratory syncytial virus RSV. Zbl 1137.92318Arenas, Abraham J.; González, Gilberto; Jódar, Lucas 10 2008 Mathematical modeling of toxoplasmosis disease in varying size populations. Zbl 1155.92336Aranda, Diego F.; Villanueva, Rafael J.; Arenas, Abraham J.; González-Parra, Gilberto C. 5 2008 On the traces of Hecke operators. Zbl 1030.11020Arenas, A. 2 2003 The simulation and interpretation of free turbulence with a cognitive neural system. Zbl 1184.76181Giralt, Francesc; Arenas, A.; Ferre-Giné, J.; Rallo, R.; Kopp, G. A. 2 2000 On the short-time dynamics of networks of Hebbian coupled oscillators. Zbl 0937.92501Pérez Vicente, C. J.; Arenas, A.; Bonilla, L. L. 8 1996 Rational equivalence of primitive integral binary quadratic forms. Zbl 0738.11035Arenas, A. 1 1991 On some equivalences of positive definite binary quadratic forms. Zbl 0691.10012Arenas, A. 2 1989 Quantitative aspects of the representations of integers by quadratic forms. Zbl 0695.10018Arenas, A. 1 1989 An arithmetic problem on the sums of three squares. Zbl 0663.10050Arenas, A. 2 1988 Arithmetic behaviour of the sums of three squares. Zbl 0623.10035Arenas, A.; Bayer, P. 2 1987 all cited Publications top 5 cited Publications all top 5 Cited by 290 Authors 14 Arenas, Abraham J. 14 González-Parra, Gilberto C. 9 Cortés López, Juan Carlos 7 Jódar Sanchez, Lucas Antonio 7 Villafuerte, Laura 6 Burgos, Clara 5 Sweilam, Nasser Hassan 5 Villanueva, Rafael-Jacinto 4 Chen-Charpentier, Benito M. 4 Ding, Xiaohua 4 Patidar, Kailash C. 3 Acedo, Luis 3 Al-saedi, Ahmed Eid Salem 3 Angstmann, Christopher N. 3 Băleanu, Dumitru I. 3 Duan, Junsheng 3 Hayat, Tasawar 3 Henry, Bruce I. 3 Ishiwata, Emiko 3 Jiang, Daqing 3 Macías-Díaz, Jorge Eduardo 3 McGann, Anna V. 3 Rach, Randolph C. 3 Sekiguchi, Masaki 2 Abdullah, Farah Aini 2 Abolghasemi, Hossein 2 Acebrón, Juan A. 2 Al-Mekhlafi, Seham Mahyoub 2 Alonso Quesada, Santiago 2 Arenas, Alex 2 Bonilla, Luis Lopez 2 Calatayud, Julia 2 Córdova-Lepe, Fernando 2 de la Sen, Manuel 2 Debbouche, Amar 2 Ding, Deqiong 2 Dlamini, Phumlani Goodwill 2 Earnest, Andrew G. 2 Fatoorehchi, Hooman 2 Gilot-Fromont, E. 2 Hölzel, Robert W. 2 Ibeas, Asier 2 Izani Ismail, Ahmad 2 Khalsaraei, Mohammad Mehdizadeh 2 Khumalo, Melusi 2 Krischer, Katharina 2 Langlais, Michel R. 2 Lélu, M. 2 Liao, Cuicui 2 Liu, Juan 2 Liu, Junli 2 Ma, Qiang 2 Mohamed, D. G. 2 Mohd, Mohd Hafiz 2 Ouifki, Rachid 2 Poulle, M.-L. 2 Rihan, Fathalla A. 2 Robledo, Gonzalo 2 Ruiz-Ramírez, Javier 2 Saad, Omar Mohamed 2 Spigler, Renato 2 Torres, Delfim Fernando Marado 2 Yang, Yu 2 Zhang, Tailei 2 Zhao, Xiaopeng 1 Abdelaziz, Mahmoud A. M. 1 Ağırağaç, Nermin 1 Aguiar, Maíra 1 Ahmad, Bashir 1 Ahmad, M. Ohmair 1 Ahmad, Riaz 1 Akuamoah, Saviour Worlanyo 1 Alharbi, Sayer Obaid 1 Alsina, Montserrat 1 Amster, Pablo 1 Anderssen, Robert Scott 1 Apeanti, Wilson Osafo 1 Aranda L., Diego F. 1 Aranda, Diego F. 1 Arenas, Abbiana R. 1 Avelar-González, F. J. 1 Avila-Vales, Eric Jose 1 Aygin, Zafer Selçuk 1 Aziz, Sara 1 Babatin, Mohammed M. 1 Bai, Zhenguo 1 Bayer Isant, Pilar 1 Bekiryazici, Zafer 1 Benincasa, Tommaso 1 Biswas, Raj Kumar 1 Blanco-Cocom, Luis D. 1 Bodzioch, Mariusz 1 Bolker, Benjamin M. 1 Bronski, Jared C. 1 Cadieu, Charles F. 1 Camacho, Jorge Fernando 1 Cardoso, Lislaine Cristina 1 Chaolu, Temuer 1 Chatzakos, Dimitrios 1 Chiranjeevi, Tirumalasetty ...and 190 more Authors all top 5 Cited in 72 Serials 9 Applied Mathematics and Computation 9 Journal of Difference Equations and Applications 8 Advances in Difference Equations 7 Computers & Mathematics with Applications 7 Journal of Computational and Applied Mathematics 6 Theoretical Population Biology 5 Chaos, Solitons and Fractals 5 Applied Mathematical Modelling 5 Computational and Applied Mathematics 4 Journal of Mathematical Analysis and Applications 4 Abstract and Applied Analysis 3 Journal of Number Theory 3 Mathematics and Computers in Simulation 3 Physica D 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Communications in Nonlinear Science and Numerical Simulation 3 Nonlinear Analysis. Real World Applications 2 Physica A 2 Physics Letters. A 2 Bulletin of Mathematical Biology 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 Mathematical Problems in Engineering 2 Discrete Dynamics in Nature and Society 2 International Journal of Applied Mathematics and Computer Science 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Journal of Applied Mathematics 2 Computational & Mathematical Methods in Medicine 1 Applicable Analysis 1 International Journal of Systems Science 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Fuzzy Sets and Systems 1 Information Sciences 1 Journal of Algebra 1 Manuscripta Mathematica 1 Bulletin of the Korean Mathematical Society 1 Applied Numerical Mathematics 1 Neural Computation 1 Applications of Mathematics 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 SIAM Journal on Applied Mathematics 1 Formal Methods in System Design 1 Journal of Mathematical Sciences (New York) 1 Chaos 1 Gravitation & Cosmology 1 Nonlinear Analysis. Modelling and Control 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Systems Science and Complexity 1 Communications on Pure and Applied Analysis 1 Journal of Applied Mathematics and Computing 1 SIAM Journal on Applied Dynamical Systems 1 Mediterranean Journal of Mathematics 1 Mathematical Biosciences and Engineering 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Journal of Biological Dynamics 1 Mathematical Modelling of Natural Phenomena 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Nonlinear Science and Applications 1 Advances in Differential Equations and Control Processes 1 International Journal for Numerical Methods in Biomedical Engineering 1 Afrika Matematika 1 Journal of Theoretical Biology 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Electronic Journal of Mathematical Analysis and Applications EJMAA 1 Journal of Mathematics 1 Mathematics 1 Sahand Communications in Mathematical Analysis 1 International Journal of Applied and Computational Mathematics 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Cited in 27 Fields 83 Biology and other natural sciences (92-XX) 69 Ordinary differential equations (34-XX) 52 Numerical analysis (65-XX) 20 Dynamical systems and ergodic theory (37-XX) 16 Probability theory and stochastic processes (60-XX) 11 Partial differential equations (35-XX) 10 Systems theory; control (93-XX) 9 Number theory (11-XX) 9 Real functions (26-XX) 9 Difference and functional equations (39-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Operator theory (47-XX) 3 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year