BVMs Bibliography

[Textbooks] [Papers] [Software]


Textbooks

  • L.Brugnano, D.Trigiante, Solving Differential Problems by Multistep Initial and Boundary Value Methods Gordon & Breach, Amsterdam, 1998.

    Papers

    Software

    Initial Value Problems


  • Iavernaro, Felice; Mazzia, Francesca, Generalization of backward differentiation formulas for parallel computers. (English) Numer. Algorithms 31, No.1-4, 139-155 (2002)

  • Iavernaro, F.; Mazzia, F. Parallel implicit predictor corrector methods. (English) Appl. Numer. Math. 42, No.1-3, 235-250 (2002).

  • Brugnano, Luigi; Trigiante, Donato Block implicit methods for ODEs. Trigiante, Donato (ed.), Recent trends in numerical analysis. Dedicated to the 65th birthday of Professor I. Galligani. Huntington, NY: Nova Science Publishers. Adv. Theory Comput. Comput. Math. 3, 81-105 (2001).

  • Di Lena, G.; Iavernaro, F. Solvability of Runge-Kutta and block-BVMs systems applied to scalar ODEs. (English) Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 513-520 (2001).

  • Aceto, L.; Amodio, P.; Brugnano, L.; Iavernaro, F.; Mazzia, F.; Trigiante, D. Study of numerical methods for evolutionary equations and construction of the corresponding software for sequential and parallel computers. Ann. Univ. Ferrara, Nuova Ser., Sez. VII 46, Suppl., 167-178 (2000).

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

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

  • Brugnano, Luigi; Trigiante, Donato Boundary value methods: The third way between linear multistep and Runge-Kutta methods. Comput. Math. Appl. 36, No.10-12, 269-284 (1998).

  • L. Brugnano. Boundary Value Methods for the Numerical Approximation of Ordinary Differential Equations, Lecture Notes in Comput. Sci. 1196 (1997) 78-89.

  • G. Di Lena, F. Iavernaro, F. Mazzia, On the unique solvability of the systems arising from Boundary Value Methods, Nonlinear Studies, Vol. 4, No. 1 (1997) pp.1-12.

  • F. Iavernaro, F. Mazzia, Convergence and stability of multistep methods solving nonlinear Initial Value Problems, SIAM Journal on Scientific Computing, 18 (1997) 270-285.

  • F. Iavernaro, F. Mazzia, Block-Boundary Value Methods for the solution of Ordinary Differential Equations. Report 16/97, Dipartimento di Matematica, Universita' di Bari (submitted).

  • L. Brugnano, D. Trigiante. On the Characterization of Stiffness for ODEs, Dynamics of Continuous, Discrete and Impulsive Systems, 2 (3) (1996) 317-335.

  • L. Brugnano, D. Trigiante. Convergence and Stability of Boundary Value Methods for Ordinary Differential Equations, J. Comput. Appl. Math. 66 (1996) 97-109.

  • P. Amodio. A-stable k-step Linear Multistep Formulae of Order 2k for the Solution of Stiff ODEs, Report 24/96 Dipartimento di Matematica, Universita' degli Studi di Bari.

  • P. Amodio, F. Mazzia, Boundary value methods based on Adams-type methods, Applied Numerical Mathematics, 18 (1995), 23-35.

  • P. Amodio, F. Mazzia, A boundary value approach to the numerical solution of initial value problems by multistep methods, Journal of Difference Equations and Applications, 1 (1995), 353-367.

  • P. Marzulli, D. Trigiante. Stability and Convergence of Boundary Value Methods for Solving ODE, J. Differ. Equations Appl. 1 (1995) 45-55.

  • P. Amodio, F. Mazzia, D. Trigiante. Stability of Some Boundary Value Methods for the Solution of Initial Value Problems, BIT, 33 (1993) 434-451.

  • L. Brugnano, D. Trigiante. Tridiagonal matrices and numerical solution of ordinary differential equations, WSSIA, 2 (1993) 71-83.

  • L. Brugnano, D. Trigiante. Stability Properties of Some BVM Methods, Appl. Num. Math. 13 (1993) 291-304.

  • L. Lopez, D. Trigiante. Boundary Value Methods and BV-Stability in the Solution of Initial Value Problems, Appl. Numer. Math. 11 (1993) 225-239.

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    Boundary Value Problems


  • Mazzia, Francesca; Trigiante, Donato A hybrid mesh selection strategy based on conditioning for boundary value ODE problems. (English) Numer. Algorithms 36, No.2, 169-187 (2004).

  • Aceto, Lidia; Mazzia, Francesca; Trigiante, Donato The performances of the code TOM on the Holt problem. (English) Antreich, K. (ed.) et al., Modeling, simulation, and optimization of integrated circuits. Proceedings of a conference, Oberwolfach, Germany, November 25-December 1, 2001. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 146, 349-360 (2003).

  • Mazzia, F.; Sgura, I. Numerical approximation of nonlinear BVPs by means of BVMs. (English) Appl. Numer. Math. 42, No.1-3, 337-352 (2002).

  • L. Brugnano, D. Trigiante. A New Mesh Selection Strategy for ODEs, Appl. Numer. Math. 24 (1997) 1-21.

  • L. Brugnano, D. Trigiante. High Order Multistep Methods for Boundary Value Problems, Appl. Num. Math. 18 (1995) 79-94.

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    Hamiltonian Problems


  • Amodio, P.; Iavernaro, F.; Trigiante, D. Conservation properties of symmetric bVMs applied to linear Hamiltonian problems. (English) Sloot, Peter M. A. (ed.) et al., Computational science - ICCS 2002. 2nd international conference, Amsterdam, the Netherlands, April. 21-24, 2002. Proceedings. Part 3. Berlin: Springer. Lect. Notes Comput. Sci. 2331, 429-438 (2002).

  • L. Brugnano. Is Symplecticness Sufficient for Approximating Hamiltonian Systems? Non-linear Differential Equations and Applications 3, 1-2 (1997) 39-48.

  • L. Brugnano. Essentially Symplectic Boundary Value Methods for Linear Hamiltonian Systems, J. Comput. Math. 15 (1997) 233-254.

  • L. Brugnano, D. Trigiante. Block Boundary Value Methods for Linear Hamiltonian Systems, Appl. Math. Comput. 81 (1997) 49-68.

  • D. Trigiante. Multipoint Methods for Linear Hamiltonian Systems, In Advances in Nonlinear Dynamics, series ``Stability and Control: Theory Methods and Applications'', Gordon & Breach, Reading (UK), (1996).

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    Differential-Algebraic Equations


  • Amodio, Pierluigi; Mazzia, Francesca An algorithm for the computation of consistent initial values for differential-algebraic equations. (English) Numer. Algorithms 19, No.1-4, 13-23 (1998).

  • Iavernaro, Felice; La Scala, Massimo; Mazzia, Francesca Boundary values methods for time-domain simulation of power system dynamic behavior. (English) IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 45, No.1, 50-63 (1998).

  • P. Amodio, F. Mazzia, An algorithm for the computation of consistent initial conditions for Differential-Algebraic equations. Report 24/97, Dipartimento di Matematica, Universita' di Bari (submitted).

  • P. Amodio, F. Mazzia, Numerical solution of differential algebraic equations and computation of consistent initial/boundary conditions. Journal of Computational and Applied Mathematics, Vol. 87/1 (1997) 135-146.

  • F. Mazzia, Boundary Value Methods for the numerical solution of Boundary Value Problems in Differential-Algebraic Equations, Bollettino dell'Unione Matematica Italiana, (7) 11-A (1997) 579-593.

  • P. Amodio, F. Mazzia. Boundary Value Methods for the Solution of Differential-Algebraic Equations, Numer. Math. 66 (1994) 411-421.

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    Partial Differential Equations


  • A. Mazzia, F. Mazzia, D. Trigiante, Boundary Value Methods for PDEs. In Proceedings of the First International Conference on Nonlinear problems in Aviation and Aerospace, S. Sivasundaram Editor, Embry-Riddle Aeronautical University Press, (1997) 421-436.

  • A. Mazzia, F. Mazzia, High-order transverse schemes for the numerical, Journal of Computational and Applied Mathematics, 82 (1-2) (1997) 299-311.

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    Sequential Implementation


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

  • P. Amodio, L. Brugnano. A Note on the Efficient Implementation of Implicit Methods for ODEs, Jour. Comput. Appl. Math. 87 (1997), 1-9.

  • P. Amodio, V. Golik, F. Mazzia, Variable step boundary value methods based on reverse Adams schemes and their grid redistribution, Applied Numerical Mathematics, 18 (1995), 5-21.

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    Parallel Implementation


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

  • P. Amodio, L. Brugnano. Parallel Implementation of Block Boundary Value Methods for ODEs, J. Comput. Appl. Math. 78 (1997) 197--211.

  • P. Amodio, M. Paprzycki. A Cyclic Reduction Approach to the Numerical Solution of Boundary Value ODEs, SIAM J. Sci. Comput. 18 (1997) 56-68.

  • P. Amodio, L. Brugnano. Parallel ODE Solvers Based on Block BVMs, Adv. Comput. Math. 7,1-2 (1997) 5--26.

  • L. Brugnano, D. Trigiante. Parallel Implementation of Block Boundary Value Methods on Nonlinear Problems: Theoric Results, Appl. Numer. Math. (to appear).

  • P. Amodio, L. Brugnano. ParalleloGAM: a Parallel Code for ODEs, Appl. Num. Math. special issue, proceedings of NUMDIFF-8, September, 1-5, 1997, Alexisbad, Germany.

  • L. Brugnano, D. Trigiante. On the Potentiality of Sequential and Parallel Codes Based on Extended Trapezoidal Rules (ETRs), Appl. Numer. Math. 25 (1997) 1-16.

  • P. Amodio, F. Mazzia, Parallel block preconditioning for the solution of boundary value methods, Journal of Computational and Applied Mathematics 69 (1996), 191-206.

  • P. Amodio, F. Mazzia, Parallel iterative solvers for boundary value methods, Mathematical and Computer Modelling 23 (1996), 29-43.

  • P. Amodio, F. Mazzia, A parallel Gauss-Seidel method for block tridiagonal linear systems, SIAM Journal on Scientific Computing, 16 (1995), 1451-1461.

  • F. Mazzia, Boundary Value Methods for Initial Value Problems: Parallel Implementation, Ann. Numer. Math. 1 (1994) 439-450.

  • P. Amodio, D. Trigiante. A Parallel Direct Method for Solving Initial Value Problems for Ordinary Differential Equations, Appl. Numer. Math. 11 (1993) 85-93.

  • L. Brugnano, F. Mazzia, D. Trigiante. Parallel Implementation of BVM Methods, Appl. Num. Math. 11 (1993) 115-124.

  • L. Brugnano, D. Trigiante. A Parallel Preconditioning Technique for BVM Methods, Appl. Num. Math. 13 (1993) 277-290.

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    Preconditioning


  • Iavernaro, F.; Trigiante, D. Preconditioning and conditioning of systems arising form boundary value methods. (English) Nonlinear Dyn. Syst. Theory 1, No.1, 59-79 (2001).

    Full paper.

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    Last Update: November, 2004