Bibliography

 

1

L. Brugnano, F. Mazzia, A parallel preconditioner for a class of M-matrices by incomplete cyclic reduction, Rapporto n. 27/90 del Dipartimento di Matematica dell'Università degli Studi di Bari.

 

 

 

2

F. Mazzia, D. Trigiante, FDSPP: a solver for singular perturbation problems, Rapporto n. 11/91 del Dipartimento di Matematica dell'Università degli Studi di Bari.

 

 

 

3

F. Mazzia, T. Politi, Numerical methods for semilinear singular perturbation problems, Rapporto n. 31/92 del Dipartimento di Matematica dell'Università degli Studi di Bari.

 

 

 

4

F. Mazzia and D. Trigiante, Numerical methods for second order singular perturbation problems, Comput. Math. Appl. 23 (1992), no. 11, 81-89.

 

 

 

5

L. Brugnano, F. Mazzia, and D. Trigiante, Parallel implementation of BVM methods, Appl. Numer. Math. 11 (1993), no. 1-3, 115-124.

 

 

 

6

P. Amodio and F. Mazzia, and D. Trigiante, Stability of some boundary value methods for the solution of initial value problems, BIT 33 (1993), no. 3, 434-451.

 

 

 

7

F. Mazzia and D. Trigiante, The role of difference equations in numerical analysis, Comput. Math. Appl. 28 (1994), no. 1-3, 209-217.

 

 

 

8

P. Amodio and F. Mazzia, Boundary value methods for the solution of differential-algebraic equations, Numer. Math. 66 (1994), no. 4, 411-421.

 

 

 

9

F. Mazzia, Boundary value methods for initial value problems: parallel implementation, Ann. Numer. Math. 1 (1994), no. 1-4, 439-450.

 

 

 

10

F. Mazzia and D. Trigiante, Numerical solution of singular perturbation problems, Calcolo 30 (1993), no. 4, 355-369 (1995).

 

 

 

11

P. Amodio and F. Mazzia, Backward error analysis of cyclic reduction for the solution of tridiagonal systems, Math. Comp. 62 (1994), no. 206, 601-617.

 

 

 

12

P. Amodio and F. Mazzia, A parallel Gauss-Seidel method for block tridiagonal linear systems, SIAM J. Sci. Comput. 16 (1995), no. 6, 1451-1461.

 

 

 

13

P. Amodio and F. Mazzia, Boundary value methods based on Adams-type methods, Appl. Numer. Math. 18 (1995), no. 1-3, 23-35.

 

 

 

14

P. Amodio, W. L. Golik, and F. Mazzia, Variable-step boundary value methods based on reverse Adams schemes and their grid redistribution, Appl. Numer. Math. 18 (1995), no. 1-3, 5-21.

 

 

15

P. Amodio and F. Mazzia, A boundary value approach to the numerical solution of initial value problems by multistep methods, J. Differ. Equations Appl. 1 (1995), no. 4, 353-367.

 

 

 

16

P. Amodio and F. Mazzia, Parallel iterative solvers for boundary value methods, Math. Comput. Modelling 23 (1996), no. 7, 29-43.

 

 

 

17

P. Amodio and F. Mazzia, Parallel block preconditioning for the solution of boundary value methods, J. Comput. Appl. Math. 69 (1996), no. 2, 191-206.

 

 

 

18

F. Iavernaro, and F. Mazzia, Convergence and stability of multistep methods solving nonlinear initial value problems, SIAM J. Sci. Comput. 18 (1997), no. 1, 270-285.

 

 

 

19

G. Di Lena, F. Iavernaro, and F. Mazzia, On the unique solvability of the systems arising from boundary value methods, Nonlinear Stud. 4 (1997), no. 1, 1-12.

 

 

 

20

P. Amodio and F. Mazzia, Parallel iterative solvers for banded linear systems, Numerical analysis and its applications (Rousse, 1996), Lecture Notes in Comput. Sci., 1196, Springer, Berlin, 1997, 17-24.

 

 

 

21

A. Mazzia and F. Mazzia, High-order transverse schemes for the numerical solution of PDEs, J. Comput. Appl. Math. 82 (1997), no. 1-2, 299-311.

 

 

 

22

A. Mazzia, F. Mazzia, and D. Trigiante, Boundary value methods for PDEs, First International Conference on Nonlinear Problems in Aviation and Aerospace (Daytona Beach, FL, 1996), Embry-Riddle Aeronaut. Univ. Press, Daytona Beach, FL, 1997, 421-436.

 

 

 

23

P. Amodio and F. Mazzia, Numerical solution of differential algebraic equations and computation of consistent initial/boundary conditions, J. Comput. Appl. Math. 87 (1997), no. 1, 135-146.

 

 

 

24

F. Mazzia, Boundary value methods for the numerical solution of boundary value problems in differential-algebraic equations, Boll. Un. Mat. Ital. A (7) 11 (1997), no. 2, 579-593.

 

 

 

25

F. Iavernaro, M. La Scala, and F. Mazzia, Boundary values methods for time-domain simulation of power system dynamic behavior, IEEE Trans. Circuits Systems I Fund. Theory Appl. 45(1998), no. 1, 50-63.

 

 

 

26

F. Iavernaro and F. Mazzia, Solving ordinary differential equations by generalized Adams methods: properties and implementation techniques, Appl. Numer. Math. 28 (1998), no. 2-4, 107-126.

 

 

 

27

P. Amodio and F. Mazzia, An algorithm for the computation of consistent initial values for differential-algebraic equations, Numer. Algorithms 19 (1998), no. 1-4, 13-23.

 

 

 

28

F. Mazzia, Loss of biorthogonality and linear system solvers, Report TR/PA/98/10 (1998) CERFACS, Toulouse, Francia.

 

 

 

29

F. Iavernaro and F. Mazzia, Block-boundary value methods for the solution of ordinary differential equations, SIAM J. Sci. Comput. 21 (1999), no. 1, 323-339.

 

 

 

30

P. Amodio and F. Mazzia, A new approach to backward error analysis of  factorization, BIT 39 (1999), no. 3, 385-402.

 

 

 

31

F. Iavernaro and F. Mazzia, On the extension of the code GAM for parallel computing., Amestoy, Patrick (ed.) et al., Euro-Par '99. Parallel processing. 5th international Euro-Par conference, Toulouse, France, August 31 – September 3, 1999. Proceedings. Lect. Notes Comput. Sci. 1685 , Springer, Berlin, 1999, 1136-1143.

 

 

 

32

F. Mazzia, QMR and selective biorthogonalization, Large-scale scientific computations of engineering and environmental problems, II (Sozopol, 1999), Notes Numer. Fluid Mech. 73, Vieweg, M. Griebel, S. Margenov, P. Yalamov eds, Vieweg, Braunschweig, 2000, 152-161.

 

 

 

33

F. Mazzia and R. A. McCoy, Numerical experiments with a shifted SSOR preconditioner for symmetric matrices, in Iterative Methods in Scientific Computation IV, David R. Kincaid and Anne C. Elster (eds.), IMACS Series in Computational and Applied Mathematics,5, International Assoc. for Mathematics and Computers in Simulation, New Brunswick, New Jersey, USA, 1999, 195-209.

 

 

 

34

F. Mazzia and D. Trigiante, Computing codes for ordinary differential equations: state of art and perspectives, Riv. Mat. Univ. Parma (6) 2* (1999), 69-87 (2000).

 

 

 

35

L. Aceto, P. Amodio, L. Brugnano, F. Iavernaro, F. Mazzia, D. Trigiante, Boundary Value Methods in Block Form: the State of the Art. Monografia n. 3 del Progetto 1998-2000 Cofinanziato dal MURST: "Analisi Numerica: Metodi e Software Matematico".

 

 

 

36

L. Aceto, P. Amodio, L. Brugnano, F. Iavernaro, F. Mazzia, and D. Trigiante, Study of numerical methods for evolutionary equations and construction of the corresponding software for sequential and parallel computers, Ann. Univ. Ferrara Sez. VII (N.S.) 46 (2000), no. suppl., 167-178.

 

 

 

37

F. Iavernaro, F. Mazzia and D. Trigiante, Phantoms and ghosts. (is the discrete world an approximation of the continuous or the other way around?), Liber amicorum, Piet van der Houwen, Herman J. J. te Riele (ed.), Ponsen & Looijen, Wageningen, 2000, 173-188.

 

 

 

38

P. Amodio, A. Bonfiglioli, P. Leggiero, F. Mazzia. Precondizionatori paralleli per la fluidodinamica computazionale., Rapporto n. 25/2003, Dipartimento Interuniversitario di Matematica, Università degli studi di Bari, 2002.

 

 

 

39

F. Iavernaro and F. Mazzia, Parallel Implicit Predictor Corrector Methods, Appl. Numer. Math., 42(2002), 235-250.

 

 

 

40

F. Iavernaro and F. Mazzia, Generalization of Backward Differentiation Formulas for parallel computers, Numerical Algorithms 31 (2002), no. 1-4, 139-155.

 

 

 

41

F. Mazzia and I. Sgura, Numerical approximation of nonlinear BVPs by means of BVMs, Appl. Numer. Math., 42(2002), 337-352.

 

 

 

42

F. Iavernaro, F. Mazzia and D. Trigiante, Eigenvalues and quasi-eigenvalues of banded Toeplitz matrices: some properties and applications, Numerical Algorithms 31(2002), no.1-4, 157-170.

 

 

 

43

L. Aceto, F. Mazzia, D. Trigiante, The performances of the code TOM on the Holt problem Modeling, simulation, and optimization of integrated circuits (Oberwolfach, 2001), Internat. Ser. Numer. Math., 146, Birkhäuser, Basel, 2003, 349-360.

 

 

 

44

F. Mazzia, D. Trigiante, A mesh selection strategy for boundary value problems, Rapporto n. 36/2003, Dipartimento di Matematica, Università degli studi di Bari, 2003.

 

 

 

45

F. Iavernaro, F. Mazzia, Test Set for Initial Value Problem Solvers Rapporto 40/2003, Dipartimento di Matematica, Università degli studi di Bari, 2003.

 

 

 

46

F. Iavernaro, F. Mazzia and D. Trigiante, On the discrete nature of physical laws, Proceedings of the Sixth International Conference on Difference Equations Augsburg, Germany 2001: New Progress in Difference Equations, Ed. Bernd Aulbach; Saber Elaydi; Gerasimos Ladas, 2004.

 

 

 

47

F.  Mazzia, D.  Trigiante, A Hybrid Mesh Selection Strategy Based on Conditioning for Boundary Value ODE Problems, Numerical Algorithms, 36 (2004), no.2, 169-187.

 

 

 

48

J. Cash, F. Mazzia, N. Sumarti, D. Trigiante, The role of conditioning in mesh selection algorithms for first order systems of linear two-point boundary value problems Journal of Computational Methods in Sciences and Engineering, to appear.