Preface to BIT 54:4

1 Collaborators for BIT volume 54

A new volume is completed, and it is time to say thank you to all, that have made this volume possible, authors, editors, printers and publishers!

But the special thank you is directed to all of you that have helped out as referees. Your work is done voluntarily as a service to the profession, and you are the ones that help us to decide which manuscripts that can be transformed into readable papers. About one manuscript in four makes it, the rest of the authors get some words on the way to get their acts together next time.

Those are the referees reporting from November 1, 2013 to October 31, 2014. Forgive me, if I missed someone deserving to be here:

Ben Adcock	Christian Bayer
Gregoire Allaire	Roland Becker
David Amsallem	Martin Berggren
Andreas Asheim	Jean-Paul Berrut
Winfried Auzinger	Timo Betcke
Constantin Bacuta	Paolo Bientinesi
Zhaojun Bai	Peter Binev
Lehel Banjai	Philipp Birken
John W Barrett	Hermann Brunner
Andrea Barth	Raimund Buerger

Carmen Rodrig Coardiel	Ernst Hairer
Mark Carpenter	Nicholas Hale
Fernando Casas	Xuli Han
Stephanie Chaillat-Loseille	Martin Hanke
Long Chen	Michael Hanke
Feng Chen	Antti Hannukainen
Yingda Cheng	Stefan Heinrich
Lucas Chesnel	Johan Helsing
Snorre H. Christiansen	Domingo Hernandez-Abreu
Eric W Chu	Holger Heumann
Matthias Chung	Hakon Hoel
Xavier Claeys	Johan Hoffman
David Cohen	Weizhang Huang
Eric Darrigrand	Daan Huybrechs
Penny Davies	Zdzislaw Jackiewicz
Oleg Davydov	Luc Jaulin
Carl de Boor	Kurt Jetter
Mehdi Dehghan	Bangti Jin
Laurent Demanet	Shi Jin
Richard Di Liu	Stephen Joe
Josef Dick	Fredrik Johansson
Boris Diskin	Andreas Karageorghis
Froilán M Dopico	Lars Karlsson
Huoyuan Duan	David I Ketcheson
Serge Dubuc	Misha Kilmer
Kenneth Duru	Othmar Koch
Matthias Ehrhardt	Yoshio Komori
Johannes Elschner	Arne Kovac
Brittany Erickson	Jeremy Kozdon
Bengt Fornberg	Gunilla Kreiss
José María Franco	JaEun Ku
Walter Gander	Patrick Kuerschner
Mahadevan Ganesh	Elisabet Larsson
Gregor Gassner	Stig Larsson
Mike Giles	Raytcho Lazarov
Ron Goldman	Jeonghun Lee
Bill Gragg	Richard Lehoucq
Thomas Grandine	Tony Lelievre
Volker Grimm	Dmitriy Leykekhman
Thomas Hagstrom	Tiejun Li

Bernt Lie	John Derwent Pryce
Fawang Liu	Panayiotis Psarrakos
Tomas Lundquist	Ronny Ramlau
Per Lötstedt	Joachim Rang
Scott Mac Lachlan	Teresa Reginska
Michael Mascagni	Nils Henrik Risebro
Stefano Maset	Siegfried M. Rump
Marie-Laurence Mazure	Jens Saak
Karl Meerbergen	Achim Schaedle
Christian Mehl	Gabriela Schranz-Kirlinger
Markus Melenk	Fiorella Sgallari
Michael Minion	Meiyue Shao
Jaun Montijano	Philip Sharp
Ron Morgan	Valeria Simoncini
Paul Muir	Alexandra Smirnova
Georg Muntingh	Hendrik Speleers
Axel Målqvist	Nicole Spillane
Ned Nedialkov	Rob Stevenson
Deanna Needell-Hunter	Martin Stynes
Michael Neilan	Hai-Wei Sun
Arnold Neumaier	Lina von Sydow
Serge Nicaise	Xue-Cheng Tai
Harald Niederreiter	Aretha Teckentrup
Freris Nikolaos	Dan Tiba
Anna Nissen	Alex Townsend
Fabio Nobile	Marnix Van Daele
Sotirios E Notaris	Arthur E P Veldman
Yvan Notay	Olivier Verdier
Paolo Novati	James H Verner
Luke Olson	Lujun Wang
Sheehan Olver	Tim Warburton
Alexander Ostermann	J.A.C. Weideman
Brynjulf Owren	Ewa Weinmüller
Kazufumi Ozawa	Holger Wendland
Beatrice Paternoster	Zhengfu Xu
Clemens Pechstein	Jinchao Xu
Francesca Pelosi	Hongguo Xu
J. M. Pena	Qianqian Yang
Per Pettersson	Chao Yang
Martin Plesinger	Mohsen Zayernouri
	Yongtao Zhang

2 Introduction to the contents of BIT 54:4

The papers we collect in this issue have been available online since more than half a year, and we get new contributions ready all the time.

These are the papers:

Winfried Auzinger, Othmar Koch, and Amir Saboor Bagherzadeh study a two point boundary value problem of an ordinary differential equation. They use a locally weighted defect for an error estimate, that can be used for adaptive mesh refinement.

Lehel Banjai and Maryna Kachanovska formulate the three-dimensional wave equation as a time-domain integral equation. It is discretized by a Runge-Kutta based convolution quadrature. The behavior of the kernel of this operator is established, and algorithms to compute the convolution weights are studied.

Alfonso Bueno-Orovio, David Kay, and Kevin Burrage study a Fourier spectral method for fractional-in-space differential equations. These equations are used to model super-diffusion effects in spatially extended structures. The method is applied to the Allen–Cahn equation for movement of phase boundaries, the FitzHugh–Nagumo model for impulse propagation in nerve membranes, and the Gray–Scott model for an autocatalytic chemical reaction.

Costanza Conti, Jean-Louis Merrien, and Lucia Romani describe an algorithm to refine a set of data vectors by repeated application of a subdivision operator to produce a sequence of even denser vector sets. New theoretical results for de Rham type Hermitian subdivisions are derived.

Catterina Dagnino, Sara Remogna, and Paul Sablonnière use spline quasi-interpolating projectors on a bounded interval, for the numerical solution of linear Fredholm integral equations of the second kind. Several algorithms are compared on a set of numerical examples.

Nicholas Hurl, William Layton, Yong Li, and Catalin Trenchea use a Crank Nicolson Leap–Frog method with the Robert Asselin Williams time filter to simulate a geophysical flow. Conditions for stability are established.

Jonas Kiessling and Raul Tempone derive error estimates of a finite difference scheme for option pricing in exponential Lévy models. Expressions are given for the dominating terms in the space and time discretization errors, when the payoff is subject to an exponential growth condition. Small jumps are approximated by a diffusion.

Yoshio Komori and Kevin Burrage derive a stochastic exponential Euler scheme for multi-dimensional, non-commutative stochastic differential equations with semilinear drift terms. Such systems are used in simulation of stiff biochemical reaction systems.

JaEun Ku studies a mixed finite element method for the primary function on unstructured meshes. It is shown that the least squares solutions are higher order perturbations of the solutions obtained by mixed and Galerkin methods. An error estimate for shape regular meshes is derived.

Abdellah Lamnii, Mohamed Lamnii, and Hamid Mraoui derive cubic spline quasi-interpolants on Powell–Sabin partitions. The coefficients of the interpolants depend only on a set of local function values and the interpolants have optimal approximation order.

Yuto Miyatake and Takayasu Matsuo describe a general framework for finding energy dissipative or conservative Galerkin schemes, and their underlying weak forms, for nonlinear evolution equations. Properties of the discrete partial derivative method are studied to establish its limits, and possible generalizations to semidiscrete dissipative schemes.

Andrew Skelton and Allan R. Willms describe an algorithm for enclosing a given set of time series data by a continuous piecewise linear band of varying height, subject to certain constraints. The band is defined by two piecewise linear curves that lie above and below the data.

That was all! I wish you all a rewarding read,

Axel Ruhe