Anna Napoli

Department of Mathematics and Computer Science - University of Calabria

Via Pietro Bucci, cubo 30/A

87036 Rende (CS) - Italy

Phone: +39 0984 496488

Fax: +39 0984 496484

Email: anna.napoli@unical.it

Research

  • Approximation of continuous functions by classic operators
  • Uniform approximations of integral functions
  • Numerical solutions of ordinary differential equations with initial and boundary conditions
  • Sequences of Polynomial Operators
  • Polynomial approximations of linear operators
  • Numerical solutions of stochastic differential equations

Publications

Peer-reviewed journal articles


2024 W. Abd-Elhameed, A. Napoli New formulas of convolved Pell polynomials, AIMS Mathematics, 9(1) (2024), 565-593.
2023 F. Costabile, M.I. Gualtieri, A. Napoli Polynomial Sequences, Basic Methods, Special Classes and Computational Applications, (Vol. 96). Walter de Gruyter GmbH & Co KG, 2023
W. Abd-Elhameed, H.M. Ahmed, A. Napoli, V. Kowalenko, New Formulas of Fibonacci Polynomials and Their Links With Orthogonal Polynomials, Symmetry 15(3) (2023), 736.
W. Abd-Elhameed, A. Napoli Some Novel Formulas of Lucas polynomials Via Different Approaches, Symmetry 15(1) (2023), 185.
2022 F. Costabile, M.I. Gualtieri, A. Napoli Towards the centenary of Sheffer polynomial sequences: old and recent results, Mathematics 2022, 10(23) (2022), 4435.
F. Costabile, M.I. Gualtieri, A. Napoli Polynomial Sequences and Their Applications. Editorial. Mathematics 2022, 10 (2022).
P.B. Helzel, A. Napoli Algoretica, Encyclopedic entry within the update volume of Enciclopedia di Bioetica e Scienza Guiridica, Edizioni Scientifiche Italiane, ESI, Napoli (2022) 1-13.
F. Costabile, M.I. Gualtieri, A. Napoli Polynomial Sequences and Their Applications, Mathematics 2022, 10(24) (2022), 4804.
F. Costabile, M.I. Gualtieri, A. Napoli General Odd and Even Central Factorial Polynomial Sequences, Mathematics 2022, 10(6), 978.
F. Costabile, M.I. Gualtieri, A. Napoli Bivariate general Appell interpolation, Numer. Algor. 9(9), 964
2021 F. Costabile, M.I. Gualtieri, A. Napoli Lidstone-Euler second type boundary value problems: theoretical and computational tools, Mediterr. J. Math. 18:180.
F. Costabile, M.I. Gualtieri, A. Napoli General bivariate Appell polynomials via matrix calculus and related interpolation hints, Mathematics 2021 9(9), 964
F. Costabile, M.I. Gualtieri, A. Napoli Lidstone-Euler interpolation and related high even order boundary value problem, Calcolo 58(2), 1-24.
2020 F. Costabile, M.I. Gualtieri, A. Napoli Lidstone-based collocation splines for odd-order BVPs, Math. Comput. Simulat. 186, 124-135.
F. Costabile, M.I. Gualtieri, A. Napoli Matrix calculus-based approach to orthogonal polynomial sequences, Mediterr. J. Math. 17:118 .
F. Costabile, M.I. Gualtieri, A. Napoli Odd and Even Lidstone-type polynomial sequences. Part 2: applications, Calcolo 57(1): 6.
2019 F.Costabile, M.I. Gualtieri, A. Napoli Polynomial sequences: elementary basic methods and application hints. A survey, RACSAM, 3829-3862.
Abd-Elhameed, A. Napoli A unified approach for solving linear and nonlinear odd-order two point boundary value problems, Bull. Malays. Math. Sci. Soc. 2019, 1-15.
2018 F. Costabile, M.I. Gualtieri, A. Napoli Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials, Mediterr. J. Math. 14(4), DOI: 10.1007/s10092-019-0354-z.
F. Costabile, M.I. Gualtieri, A. Napoli Odd and Even Lidstone-type polynomial sequences. Part 1: basic topics, Advances in Difference Equations 2018(1), 299.
F. Costabile, M.I. Gualtieri, A. Napoli Some results on generalized Szász operators involving Sheffer polynomials, J. Comp. Appl. Math. 337, 244-255.
A. Napoli, W. Abd-Elhameed A new collocation algorithm for solving even-order boundary value problems via a novel matrix method, Integral Transform. and Spec. Funct., 30(2), (2018), 112-127.
2017 A. Napoli, W. Abd-Elhameed An Innovative Harmonic Numbers Operational Matrix Method for Solving Initial Value Problems, CALCOLO 54(1), 57-76, DOI: 10.1007/s10092-016-0176-1.
F. Costabile, A. Napoli A class of Birkhoff-Lagrange collocation methods for high order boundary value problems, Appl. Numer. Math. 116, 129-140.
A. Napoli, W. Abd-Elhameed Numerical solution of eighth-order boundary value problems by using Legendre polynomials, Int. J. Comp. Meth. 14(7), 1750083 (19 pages), DOI: 10.1142/S0219876217500839.
F. Costabile, M.I. Gualtieri, A. Napoli Relationships between Interpolation and Differential Equations. A Class of Collocation Methods, in Dynamical Systems - Analytical and Computational Techniques, InTech, ISBN 978-953-51-3015-4-2, DOI: 10.5772/66995 (2017).
2016 A. NAPOLI Solutions of linear second order initial value problems by using Bernoulli polynomials, Appl. Numer. Math. 99, 109-120, DOI: 10.1016/j.apnum.2015.08.011.
F. Costabile, A. Napoli A new spectral method for a class of linear boundary value problems, J. Comp. Appl. Math. 292, 329-341 DOI: 10.1016/j.cam.2015.07.015.
2015 F. Costabile, A. Napoli A multipoint Birkhoff type boundary value problem, J. Numer. Math 23(1)
F. Costabile, A. Napoli A method for high-order multipoint boundary value problems with Birkhoff-type conditions, Int. J. Comput. Math. 92 (1), 192-200.
F. Costabile, A. Napoli Collocation for high order differential equations with Hermite boundary conditions, Appl. Numer. Math. 87, 157-167.
2014 F. Costabile, A. Napoli Numerical solution of high order Bernoulli boundary value problems, J. Appl. Math., Vol. 2014 Article ID 276585, 9 pages.
2012 F. Costabile, A. Napoli Collocation for high order differential equations with Lidstone boundary conditions, J. Appl. Math., vol. 2012, Article ID 120792, doi:10.1155/2012/120792 (2012).
A. Napoli On a class of stochastic Runge Kutta methods, Int. J. Contemp. Math. Sciences 7(36), 1757-1769.
2011 F. Costabile, A. Napoli Economical Runge-Kutta methods with strong order one for stochastic differential equations Appl. Numer. Math. 61, 160-169.
F. Costabile, A. Napoli A class of collocation methods for numerical integration of initial value problems, Comput. Math. Appl. 62(8), 3221-3235.
F. Costabile, A. Napoli A Mathematica package for the solution of IVPs, Int. J. Numer. Meth. Appl. 6(2), 123-136.
A. NAPOLI Numerical solution of high order differential equations with Bernoulli boundary conditions, Proceedings of the 2011 International Conference on Mathematical Methods in Science and Engineering, Benidorm, Spain, 26-30 June 2011, Vol.3, ISBN 978-84-614-6167-7.
2010 F. Costabile, A. Napoli Special even polynomials and related interpolatory problems, Integral Transforms Spec. Funct. 21(3), 183-196.
A. Napoli Economical Runge-Kutta methods with weak second order for stochastic differential equations, Int. J. Contemp. Math. Sciences 5(24) (2010) 1151-1160.
F. Costabile, A. Napoli New kernels of Sard type and applications Rend. Circ. Mat. Palermo (2), Suppl. 82, 407-420
A. Napoli La sezione aurea: un'occasione per l'interdisciplinarità, Didattica e didattiche disciplinari 9,73-94
2009 F. Costabile, A. Napoli A special class of polynomials related to non classic general interpolatory problems, Integral Transforms Spec. Funct. 20(7) (2009) 539-550.
2008 F. Costabile, A. Napoli Economical Runge-Kutta methods for numerical solution of stochastic differential equations, BIT 48(3), 499-509.
F. Costabile, M.I. Gualtieri, A. Napoli Il concetto di integrale col supporto di MatCos, Didattica e didattiche disciplinari 6, 107-126.
M.I. Gualtieri, A. Napoli Rodonee e... simili, Progetto Alice, Vol. IX (27), 523-538
2007 F. Costabile, A. Napoli A collocation method for global approximation of general second order BVPs, Computing Letters 3(1), 23-34, DOI: 10.1163/157404007779994205.
F. Costabile, A. Napoli Solving BVPs Using Two-point Taylor Formula by a symbolic software, J. Comp. Appl. Math. 210(1-2), 136-148, DOI: 10.1016/j.cam.2006.10.081.
M.I. Gualtieri, A. Napoli Un percorso didattico sull?integrazione numerica, Didattica delle Scienze e Informatica nella Scuola, 251, Ottobre 2007.
2006 F. Costabile, A. Napoli A method for polynomial approximation of the solution of general second order BVPs, Far East J. Appl. Math., 25(3), 289-305
2005 F. Costabile, A. Napoli A Mathematica package for the solution of Ordinary Differential Equations using Taylor Series method In: Lecture Series on Computer and Computational Sciences, Vol. 4 A, (2005) 131-134.
2004 F. Costabile, A. Napoli Stability of Chebyshev collocation method, Comput. Math. Appl. 47(4-5), 659-666.
F. Costabile, A. Napoli A method for global approximation of the solution of second order IVPs, Rend. Mat. Appl. VII. Ser. 24.
2001 F. Costabile, A. Napoli A method for global approximation of the initial value problem, Numer. Algorithms 27(2). 119-130.
1999 A. Napoli A method for global approximation of the Cauchy differential problem by Chebyshev polynomials of first kind, Atti del XVI Congresso U.M.I., Napoli, September 1999.

Conference Papers


2024 - The parabolic mean operator and applications, Functional Analysis: Methods, and Applications (FAMA2024), Amantea (CS), June 6-8, 2024.
2024 - The parabolic mean operator and the related polynomial sequences, AMCSE 4th International Conference on Applied Mathematics, Computational Science and Systems Engineering, London, UK, April 29 - May 1, 2024.
2023 - Appell-type Quadrature Formulas, Calcolo Scientifico e Modelli Matematici, Naples, Italy, January 29-31, 2023.
2023 - Umbral Quadrature Formulas, International Conference on Approximation Theory and Applications, Cetraro (CS), Italy, June 18-22, 2023.
2019 - Spline solution of odd-order Lidstone-type BVPs, International Conference Mathematical And Computational Modelling, Approximation And Simulation (MACMAS 2019), Granada Spain, September 9-11, 2019.
2017 Collocation spline interpolation for numerical solution of high-order Lidstone-type Boundary Value Problems, Foundations of Computational Mathematic (FOCM 2017), Barcelona, Spain, July 10-19, 2017.
2015 Numerical solution of initial value problems by using Legendre polynomials, Workshop on Numerical Modeling in Evolutionary problems: perspectives and applications (NUMEP 2015), Fisciano (SA), October 26-27, 2015.
A class of Lagrange-collocation methods for high order boundary value problems, New trends in Numerical Analysys: Theory, Methods, Algorithms and Applications (NETNA 2015), Falerna (CZ), June 18-21, 2015
2011 Numerical solution of high order differential equations with Bernoulli boundary conditions, International Conference on Mathematical Methods in Science and Engineering (CMMSE 2011), Benidorm, Spain, June 26-30, 2011
2009 New kernels of Sard type and applications, FAAT – 6th International Conference on Functional Analysis and Approximation Theory, Acquafredda di Maratea (PZ), September 24-30, 2009
R. Caira, M.I. Gualtieri, R. Mazza, A. Napoli, R. Trunfio, Seeking the optimal schedule by simulation in logistic, Fifth International Winter Conference of the Italian Association of Operations Research, Cortina d'Ampezzo (BL) – Italy, January 26-30, 2009
2006 La sezione aurea, Cattedra “Matematica oggi”, Fondazione Guarasci, Cosenza, March 9, 2006
2005 A Mathematica package for the solution of Ordinary Differential Equations using Taylor Series method, International Conference of Computational Methods in Sciences and Engineering 2005 (ICCMSE 2005), Corinto, Greece October 21-26, 2005
Solving BVPs Using Two-point Taylor formula by a symbolic software, International Congress: Numerical Analysis: the state of the art, Rende (CS), University of Calabria, May 19-21, 2005
2002 A method for global approximation of the solution of second order IVPs, National Congress: Analisi Numerica: stato dell’arte, Rende (CS), September 26-28, 2002
2001 Galerkin type methods with Chebyshev nodes for IVPs, Workshop on Numerical Methods for evolutionary Problems, Peschici (FG), September 2001
1999 Matematica e software, IX Settimana della cultura scientifica e tecnologica, Reggio Calabria, April 14, 1999
1998 Multimedialità nella didattica, VIII settimana della cultura scientifica e tecnologica, Catanzaro, March 23, 1998

Books


2023 F.A. Costabile, M.I. Gualtieri, A. Napoli Polynomial Sequences, Basic Methods, Special Classes and Computational Applications, (Vol. 96), Walter de Gruyter GmbH & Co KG, 2023
2008 R. Caira, M.I. Gualtieri, A. Napoli Restart con Maple, Teoria ed esercizi, Ed. Aracne, Roma, 2008

Other articles (Technical reports and non-peer reviewed publications)


2006 F. Costabile, A. Napoli Approximate solution of general second order BVPs, LAN (Unical) Pubblication n. 17 (2006)
F. Costabile, A. Napoli A Matlab code for general second order boundary value problems, LAN (Unical) Pubblication n. 16 (2006)
2005 F. Costabile, A. Napoli Corso propedeutico AA 2005-06 – Relazione finale, CIRD (Unical) Pubblication n. 47, (2005)
2004 F. Costabile, A. Napoli Solving IVPs and BVPs Using Taylor Series by Mathematica, LAN (Unical) Pubblication n. 13 (2004)
2003 M.I. GualtieriI, A. Napoli Integrazione numerica: una proposta di unità didattica, CIRD (Unical) Pubblication n. 8, (2003)
2002 F. Costabile, A. Napoli A Galerkin-type method for global approximation of second order IVPs, LAN (Unical) Pubblication n. 2, (2002)
2001 F. Costabile, A. Napoli Matematica e computer con MatCos. Esperienze nelle classi, CIRD Technical report n.32 - Unical (2001)
F. Costabile, A. Napoli A Galerkin-type method with Chebyshev nodes for IVPs, Technical report n.41 Series II – Unical (2001)
1999 F. Costabile, A. Napoli A global method for approximation of the Cauchy differential problem by Chebyshev polynomilas of the second kind, LAN, Technical report n.37 Series II – Unical (1999)
1998 F. Costabile, A. Napoli A method for global approximation of the Cauchy differential problem, LAN, Technical report n.34 Series II – Unical (1998)
1996 F. Costabile, A. Napoli Un metodo per l’integrazione indefinita, LAN, Technical report n.24 Series II – Unical (1996)
1995 A. Napoli Polinomi di Bernstein e questioni connesse, LAN, Technical report n.17 Series II – Unical (1995)

Referee/Review activities

  • Applied Mathematics and Computation (AMC)
  • Applied Numerical Mathematics
  • Boundary Value Problems
  • Computer Modeling in Engineering & Sciences (CMES)
  • Dolomites Research Notes on Approximation
  • Fractal and Fractional
  • International Journal of Applied and Computational Mathematics (IACM)
  • International Journal of Applied and Computational Methods (IJCM)
  • Iranian Journal of Science and Technology
  • Journal of Inequalities and Applications
  • Mathematics and Computers in Simulation (MATCOM)
  • Mediterranean Journal of Mathematics (MJOM)
  • Numerical Algorithms
  • Numerical Methods for Partial Differential Equations
  • Symmetry

Software

2005 A. Napoli TaylorMeth (A Mathematica package for the solution of BVPs)
2005 A. Napoli The Matlab solver BVMC (Software for Boundary Value Problems)

Recent Conferences and Workshops

2024 Functional Analysis: Methods, and Applications (FAMA2024)
Amantea (CS), Italy, June 6-8, 2024
Poster: The parabolic mean operator and applications
2024 AMCSE 4th International Conference on Applied Mathematics, Computational Science and Systems Engineering
London, UK, April 29 - May 1, 2024
Poster: The parabolic mean operator and the related polynomial sequences
2023 Calcolo Scientifico e Modelli Matematici
Naples, Italy, January 29-31, 2023
Poster: Appell-type Quadrature Formulas
2023 International Conference on Approximation Theory and Applications
Cetraro (CS), Italy, June 18-22, 2023
Poster: - Umbral Quadrature Formulas
2019 International Conference on Mathematical and Computational Modelling Approximation and Simulation (MACMAS 2019)
Granada, Spain, 9-11 September 2019
Poster: Spline collocation for odd-order Lidstone-type BVPs
2017 Foundation of Computational Mathematics (FoCM2017)
Barcelona, Spain, 10-19 July 2017
Poster: Collocation spline interpolation for high-order Lidstone-type boundary value problems
2015 Numerical Modeling in Evolutionary Problems: Perspectives and Appl. Workshop (NUMEP2015)
Fisciano (SA), Italy, 26-27 October 2015
Numerical solution of initial value problems by using Legendre polynomials
2015 New Trends in Numerical Analysis. Theory, Methods, Algor. and Appl. Intern. Conf. (NETNA2015)
Falerna (CZ), Italy, 18-21 June 2015
A class of Lagrange-collocation methods for high order boundary value problems
Scientific and Organizing Committee

Teaching Activities a.a. 2019-2020

Analisi Numerica 2 (CdS Magistrale in Matematica)
Department of Mathematics and Computer Science
University of Calabria
Calcolo Numerico e Programmazione (CdS Triennale in Matematica)
Department of Mathematics and Computer Science
University of Calabria
Matematica e Statistica applicate alla Biologia (CdS Magistrale in Biologia)
Department of Biology, Ecology and Earth Sciences
University of Calabria
Matematica (CdS in Chimica e Tecnologia Farmaceutiche)
Department of Pharmacy, Health and Nutritional Sciences
University of Calabria