Second Symposium on “Recent Trends in the Numerical Solution ofDifferential Equations”: PrefaceLuigi Brugnano Citation: AIP Conf. Proc. 1168, 705 (2009); doi: 10.1063/1.3241563 View online: http://dx.doi.org/10.1063/1.3241563 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1168&Issue=1 Published by the American Institute of Physics. Related ArticlesRashba spin-orbit effect on tunneling time in graphene superlattice J. Appl. Phys. 111, 093724 (2012) Frequency control in the process of a multicell superconducting cavity production Rev. Sci. Instrum. 83, 043304 (2012) Counting the exponents of single transfer matrices J. Math. Phys. 52, 063501 (2011) Communities in multislice voting networks Chaos 20, 041108 (2010) On alphabetic presentations of Clifford algebras and their possible applications J. Math. Phys. 50, 123523 (2009) Additional information on AIP Conf. Proc.Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

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Second Symposium on "Recent Trends in the Numerical Solution of Differential Equations": Preface

Luigi Bmgnano

Dipartimento diMatematica "U. Dini", Viale Morgagni 67/A, 50134 Firenze (Italy) http://www.math.unifi.it/~brugnano/

Most of the topics covered by this symposium deal with the numerical solution of ODE-IVPs, a field of research in which many contributions are due to Ernst Hairer, whose 60f/z birthday is celebrated in this 2009 edition of ICNAAM. In particular, there are a number of talks devoted to the numerical solution of Hamiltonian problems, one of the Ernst's favourite field of investigation, in recent years.

Many topics are, however, covered by the talks in this second edition of the symposium, which can be roughly collected as foUows:

• numerical methods for Hamiltonian problems (papers 1, 3, 5, and 9); • numerical methods for ODE-BVPs (papers 2 and 12); • numerical methods for problems deriving from the semi-discretization of PDEs (papers 4 and 10); • numerical solution of DAEs (paper 6); • a new definition of stiffness with applications (paper 7); • numerical methods for dynamical systems possessing a Lyapunov function (paper 8); • numerical methods for variational inequafities (paper 11).

In the foUowing, we briefly describe the contents of the various papers, fisted in alphabetical order of the respective speakers.

Paper 1, by L. Aceto and D. Trigiante. The authors study the possibility of obtaining discrete periodic or quasi-periodic solutions when approximating Hamiltonian problems, in order to avoid a possible drift in the Hamiltonian function. They highlight the existing connections with a classical problem of evolution of planar polygons.

Paper 2, by P. Amodio and G. Settanni. Here, it is studied a cheap error estimate, when using generafized upwind methods for solving second-order BVPs. The considered methods discretize directly higher-order derivatives by means of suitable Boundary Value Methods (B VMs).

Paper 3, by L. Brugnano, F. lavemaro, and D. Trigiante. The authors describe the newly introduced class of methods caUed Hamiltonian BVMs (HBVMs), able to numerically preserve polynomial Hamiltonians (see also paper 5). The presented methods can be also regarded as a generalization of collocation methods.

Paper 4, by S. Gonz^les-Pinto and S.P6rez-Rodrigues. Here, in the framework of MoL, the authors study time-adaptive Radau methods for Advection-Diffusion-Reaction PDEs. The presented approach is numerically com­pared with other known solvers.

Paper 5, by L. Brugnano, F. lavemaro, and T. Susca. The authors describe the efficient implementation of HBVMs, the methods presented in paper 3. Such methods are able to numerically preserve polynomial Hamiltonian functions by means of the infi-oduction of a suitable number of "silent stages".

Paper 6, by R. Lamour and D. Monett Diaz. Here, the efficient use of Automatic-Differentiation is studied for index determination, in connection with the numerical solution of DAEs. Comparisons with other index determination algorithms, on an illustrative example, are given.

Paper 7, by L. Brugnano, F. Mazzia, and D. Trigiante. The authors describe a very general definition of stiffiiess, and its impact when designing numerical codes for ODEs. The new definition encompasses all the previous ones, and naturaUy extends to BVPs.

CPl 168, Vol. 2, Numerical Analysis and Applied Mathematics, International Conference 2009 edited by T. E. Simos, G. Psihoyios, and Ch. Tsitouras

O 2009 American Institute of Physics 978-0-7354-0708-4/09/$25.00

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Paper 8, by M. Calvo, P. Laburta, J.I. Montijano, L. Randez. Here, the authors study efficient Runge-Kutta methods, provided with a continuous extension and a projection technique, in order to efficiently integrate ordinary differential equations with a known Lyapunov function.

Paper 9, by E. Celledoni, R. McLachlan, B.Owren, and R. Quispel. The authors study the structure of B-series for integrators which are conjugate to symplectic or energy preserving methods, proposing to study the modified vector fields of such methods as filtrations.

Paper 10, by M.Calvo, J.M.Franco, J.I. Montijano, and L.Randez. In this paper, new finite difference schemes for the spatial discretization and time advancing RK schemes for the numerical simulation of Computational Aero-Acoustic problems are studied.

Paper 11, by L. Brugnano and A. Sestini. The authors present the efficient modeling of obstacle problems by means of the so called "Piecewise Linear Systems". The latter are linear systems, whose coefficient matrix is a piecewise constant function of the solution itself.

Paper 12, by M. Van Daele, D. Hollevoet, and G. Vanden Berghe. Here, multiparameter exponentially-fitted Numerov methods applied to second-order boundary value problems are analysed. In particular, the proposed approach is aimed to overcome some drawbacks of classical exponentially-fitted methods.

Luigi Brugnano

Luigi Brugnano is professor of Numerical Analysis at the University of Florence, Italy. He graduated "magna cum laude" at the Univeristy of Bari, Italy, in 1985. At the same University he started his scienfific activity, under the guidance of professor Donato Trigiante and, in 1990, he became researcher at that University. In 1992 he moved to the University of Florence as an associate professor and, in 2001, he became full professor. His scientific activity has focused on several topics, such as: numerical linear algebra, numerical methods for polynomial roots, numerical methods for differential equations, parallel computing, numerical software, and mathematical modelling. He is author of about 70 scientific publications, including three monographs.

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