@COMMENT{{{This file has been generated by bib2bib 1.75}}
@COMMENT{{{Command line: bib2bib -c '$key="shardlow00:_stoch_allen_cahn" or $key="gilsing05:_sdelab_matlab" or $key="blowey03:_front" or $key="mackay:94" or $key="shardlow05:_numer_pdes" or $key="mccm:455" or $key="aczon:1997" or $key="shardlow:2003" or $key="shardlow05:_weak" or $key="shardlow:1999a" or $key="mills06:_comput_geodes_inter_splin" or $key="shardlow:97" or $key="shardlow04:_nucleat_pde" or $key="shardlow04:_modif_equat" or $key="shardlow02:_cahn_hilliar" or $key="shardlow03:_split" or $key="shardlow01:_stoch_allen_cahn" or $key="shardlow04:_geomet" or $key="shardlow:93" or $key="shardlow:1997" or $key="lord05:_post" or $key="shardlow:1996" or $key="shardlow:99" or $key="shardlow00:_pertur_theor" or $key="buckwar05:_weak_euler_schem_stoch_differ_delay_equat" or 1=2' /home/shardlow/common/tex/inputs/ref.bib}}
@BOOK{blowey03:_front,
TITLE = {Frontiers in numerical analysis},
SERIES = {Universitext},
EDITOR = {Blowey, James F. and Craig, Alan W. and Shardlow, Tony},
NOTE = {Papers from the 10th LMS-EPSRC Numerical Analysis Summer
School held at the University of Durham, Durham, July 7--19,
2002},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = 2003,
PAGES = {xiv+349},
ISBN = {3-540-44319-3},
MRCLASS = {65-06},
MRNUMBER = {2004d:65003}
}
@ARTICLE{mackay:94,
AUTHOR = {MacKay, Robert S. and Shardlow, Tony},
TITLE = {The multiplicity of bifurcation for area preserving
mappings},
JOURNAL = {Bull. LMS},
FJOURNAL = {Bulletin London Mathematics Society},
YEAR = 1994,
VOLUME = 4,
PAGES = {382--394}
}
@ARTICLE{gilsing05:_sdelab_matlab,
AUTHOR = {Hagen Gilsing and Tony Shardlow},
TITLE = {{SDELab}: a package for solving stochastic differential equations in {MATLAB}},
YEAR = 2006,
NOTE = {Available as MIMS EPrint 2006.1, Manchester Institute for
Mathematical Sciences, The University of Manchester, UK},
JOURNAL = {To appear in J. Comput. Appl. Math. 21 pages.},
URL = {http://130.88.123.127/134/},
ABSTRACT = {
We introduce SDELab, a package for solving stochastic differential
equations (SDEs) within MATLAB. SDELab features explicit and
implicit integrators for a general class of Ito and Stratonovich
SDEs, including Milstein's method, sophisticated algorithms for
iterated stochastic integrals, and flexible plotting facilities.}
}
@INCOLLECTION{mills06:_comput_geodes_inter_splin,
AUTHOR = {Anna Mills and Stephen Marsland and Tony Shardlow},
TITLE = {Computing the {Geodesic Interpolating Spline}},
BOOKTITLE = {Biomedical Image Registration},
PAGES = {169--},
PUBLISHER = {Springer},
YEAR = 2006,
EDITOR = {J. P. W. Pluim and B. Lika and F. A. Gerritsen},
VOLUME = 4057,
SERIES = {LNCS},
URL = {http://130.88.123.127/138/},
ABSTRACT = {We examine non-rigid image registration by knotpoint
matching. We consider registering two images, each with a set of
knotpoints marked, where one of the images is to be registered to the
other by a nonlinear warp so that the knotpoints on the template image
are exactly aligned with the corresponding knotpoints on the reference
image.
We explore two approaches to computing the Geodesic Interpolating
Spline registration. First, we describe a method which exploits the
structure of the objective function and constraints to permit
efficient optimisation and second, we outline an approach using the
framework of classical mechanics.}
}
@ARTICLE{buckwar05:_weak_euler_schem_stoch_differ_delay_equat,
AUTHOR = {Evelyn Buckwar and Rachel Kuske and Salah-Eldin Mohammed and Tony
Shardlow},
TITLE = {The Weak {Euler} Scheme for Stochastic
Differential Delay Equations},
NOTE = {Available as MIMS EPrint 2006.2, Manchester Institute for
Mathematical Sciences, The University of Manchester, UK},
JOURNAL = {Submitted to Mathematics of
Computation},
YEAR = 2006,
ABSTRACT = {We develop a weak numerical Euler scheme for non-linear stochastic delay differential equations (SDDEs) driven by multidimensional Brownian motion. The weak Euler scheme has
order of convergence 1, as in the case of stochastic ordinary
differential equations (SODEs) (i.e., without delay).The result
holds for SDDEs with multiple finite fixed delays in the drift and
diffusion terms. Although the set-up is non-anticipating,
our approach uses the Malliavin calculus and the
anticipating stochastic analysis techniques of Nualart
and Pardoux.},
URL = {http://130.88.123.127/149/}
}
@ARTICLE{lord05:_post,
AUTHOR = {Gabriel Lord and Tony Shardlow},
TITLE = {Post processing for stochastic parabolic partial differential
equations},
NOTE = {Available as MIMS EPrint 2006.3, Manchester Institute for
Mathematical Sciences, The University of Manchester, UK},
JOURNAL = {To Appear, SIAM J. Num. Anal.},
YEAR = 2006,
ABSTRACT = {We investigate the strong approximation of stochastic parabolic
partial differential equations with additive noise. We introduce
post-processing in the context of a standard Galerkin approximation,
although other spatial discretisations are possible. In time, we
use an
exponential integrator. We prove strong error estimates
and discuss the best number of post-processing terms to take.
Numerically, we evaluate the efficiency of the methods and observe
rates of convergence. Some experiments with the implicit
Euler--Maruyama method are described.},
URL = { http://130.88.123.127/137/}
}
@ARTICLE{shardlow04:_modif_equat,
AUTHOR = {Shardlow, Tony},
TITLE = {Modified Equations for Stochastic Differential Equations},
YEAR = 2006,
MONTH = {March},
JOURNAL = {BIT Numerical Mathematics},
URL = {http://dx.doi.org/10.1007/s10543-005-0041-0 },
ABSTRACT = {We describe a backward error analysis for stochastic differential equations with respect to weak convergence. Modified equations are provided for forward and backward Euler approximations to Ito SDEs with additive noise, and extensions to other types of equations and approximation discussed.},
URL = {http://www.maths.man.ac.uk/~nareports/narep455.pdf}
}
@ARTICLE{shardlow00:_stoch_allen_cahn,
AUTHOR = {Shardlow, Tony},
TITLE = {Stochastic perturbations of the {A}llen-{C}ahn equation},
JOURNAL = {Electron. J. Differential Equations},
FJOURNAL = {Electronic Journal of Differential Equations},
YEAR = 2000,
VOLUME = 47,
PAGES = {19 pages},
ISSN = {1072-6691},
MRCLASS = {74N20 (34F05 35B25 35R60 60H15)},
MRNUMBER = {2001k:74082},
MRREVIEWER = {Thomas Wanner},
URL = {http://www.maths.man.ac.uk/~shardlow/papers/allen.pdf}
}
@INPROCEEDINGS{shardlow01:_stoch_allen_cahn,
AUTHOR = {Shardlow, Tony},
TITLE = {Stochastic {Allen-Cahn}: analysis and numerics},
BOOKTITLE = {Workshop on Stochastic Partial Differential Equations},
EDITOR = {Marianne Huebner and Michael Sorensen},
YEAR = 2001,
NUMBER = 20,
ORGANIZATION = {Centre for Mathematical Physics and Stochastic - MaPhySto},
PUBLISHER = {University of Copenhagen},
SERIES = {Proceedings of workshop held at University of Copenhagen January 4-6, 2001}
}
@ARTICLE{shardlow02:_cahn_hilliar,
AUTHOR = {Shardlow, Tony},
TITLE = {A coupled {C}ahn-{H}illiard particle system},
JOURNAL = {Electron. J. Differential Equations},
FJOURNAL = {Electronic Journal of Differential Equations},
YEAR = 2002,
PAGES = {21 pages },
VOLUME = 73,
ISSN = {1072-6691},
MRCLASS = {35R60 (35B25 35K55 60H15)},
MRNUMBER = {2003f:35294},
MRREVIEWER = {Jan I. Seidler},
URL = {http://ejde.math.swt.edu/Volumes/2002/73/abstr.html}
}
@ARTICLE{shardlow04:_nucleat_pde,
AUTHOR = {Shardlow, Tony},
TITLE = {Nucleation of waves in excitable media by noise},
ABSTRACT = {We are interested in reaction-diffusion equations that model excitable media under the influence of an additive noise. In many models of this type, the homogeneous zero state is stable, and interesting dynamics are observed only for certain initial data. In the presence of noise, the excitable media is stimulated, and the noise may be sufficiently large to nucleate wave forms. In computations, we see for small noise that only target waves are nucleated when the time scales for excitation and inhibition are sufficiently separated. We provide a theorem that supports this observation. },
JOURNAL = {SIAM Multiscale Model. Simul.},
VOLUME = 3,
NUMBER = 1,
PAGES = {151--167},
YEAR = 2004,
URL = {http://epubs.siam.org/sam-bin/dbq/article/60214}
}
@ARTICLE{shardlow03:_split,
AUTHOR = {Shardlow, Tony},
TITLE = {Splitting for dissipative particle dynamics},
ABSTRACT = {We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers.},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = 24,
YEAR = 2003,
NUMBER = 4,
PAGES = {1267--1282},
ISSN = {1095-7197},
MRCLASS = {60H10 (60K35 82C80)},
MRNUMBER = {2004d:60157},
URL = {http://epubs.siam.org/sam-bin/dbq/article/39287}
}
@ARTICLE{shardlow04:_geomet,
AUTHOR = { Shardlow, Tony and Yan, Yubin},
TITLE = {Geometric ergodicity for dissipative particle dynamics},
ABSTRACT = {Dissipative particle dynamics is a system of
stochastic differential equations modelling complex fluid flows. We
consider the problem of $N$ particles evolving on the one
dimensional periodic domain of length $L$ and, if the density of
particles is large, prove geometric convergence to a unique
invariant measure. The proof uses minorization and drift arguments,
but allows elements of the drift and diffusion matrix to have
compact support where hypoellipticity arguments are not directly
available.},
JOURNAL = {Stochastics and Dynamics},
VOLUME = 6,
NUMBER = 1,
PAGES = {31 pages},
MONTH = {March},
YEAR = 2006,
URL = {http://www.maths.man.ac.uk/~shardlow/papers/dpd_erg_web.pdf}
}
@ARTICLE{shardlow05:_numer_pdes,
AUTHOR = {Shardlow, Tony},
TITLE = {Numerical simulation of stochastic {PDE}s for excitable media},
ABSTRACT = {We discuss the numerical solution of a number of stochastic perturbations of the Barkley model of excitable media, widely used in the study of spiral waves. Two numerical methods are considered for solving this equation, one based on Barkley's original formulation and one based on spectral methods. It is found to be beneficial to modify the nonlinearity describing the reaction kinetics. An efficient method of approximating the Wiener process is presented. The effectiveness of the methods depends on the stochastic PDE under consideration. },
FJOURNAL = {Journal of Computational and Applied Mathematics},
JOURNAL = {J. Comput. Appl. Math.},
VOLUME = 175,
NUMBER = 2,
MONTH = {March},
PAGES = {429--446},
YEAR = 2005,
URL = {http://dx.doi.org/10.1016/j.cam.2004.06.020}
}
@ARTICLE{shardlow:1996,
AUTHOR = {Shardlow, Tony},
TITLE = {Periodic orbits and unstable manifolds},
OPTCROSSREF = {},
OPTKEY = {},
FJOURNAL = {Numerical Functional Analysis and Optimization},
JOURNAL = {Numer. Funct. Anal. Optim.},
YEAR = {1996},
VOLUME = {17},
NUMBER = {9--10},
PAGES = {963--989},
OPTMONTH = {},
OPTNOTE = {},
OPTANNOTE = {}
}
@ARTICLE{shardlow:1997,
AUTHOR = {Shardlow, Tony},
TITLE = {Inertial Manifolds and Linear Multistep Methods},
OPTCROSSREF = {},
OPTKEY = {},
FJOURNAL = {Numerical Algorithms},
JOURNAL = {Numer. Algorithms.},
YEAR = {1997},
VOLUME = {14},
NUMBER = {1--3},
PAGES = {189--209},
OPTMONTH = {},
OPTNOTE = {},
OPTANNOTE = {}
}
@ARTICLE{shardlow00:_pertur_theor,
AUTHOR = {Shardlow, Tony and Stuart, Andrew M.},
TITLE = {A Perturbation Theory for Ergodic Properties of
{Markov} Chains},
ABSTRACT = {Perturbations to Markov chains and Markov processes are considered. The unperturbed problem is assumed to be geometrically ergodic in the sense usually established through the use of Foster--Lyapunov drift conditions. The perturbations are assumed to be uniform, in a weak sense, on bounded time intervals. The long-time behavior of the perturbed chain is studied. Applications are given to numerical approximations of a randomly impulsed ODE, an Ito stochastic differential equation (SDE), and a parabolic stochastic partial differential equation (SPDE) subject to space-time Brownian noise. Existing perturbation theories for geometrically ergodic Markov chains are not readily applicable to these situations since they require very stringent hypotheses on the perturbations.},
JOURNAL = {SIAM J. Numer. Anal.},
YEAR = {2000},
OPTKEY = {},
VOLUME = {37},
NUMBER = {4},
PAGES = {1120--1137},
OPTMONTH = {},
OPTNOTE = {},
OPTANNOTE = {},
URL = {http://epubs.siam.org/sam-bin/dbq/article/33723}
}
@ARTICLE{shardlow:1999a,
AUTHOR = {Shardlow, Tony},
TITLE = {Numerical methods for stochastic parabolic
{P}{D}{E}s},
JOURNAL = {Numer. Funct. Anal. Optim.},
FJOURNAL = {Numerical Functional Analysis and Optimization. An
International Journal},
VOLUME = 20,
YEAR = 1999,
NUMBER = {1-2},
PAGES = {121--145},
ISSN = {0163-0563},
CODEN = {NFADOL},
MRCLASS = {65C30 (60H35 65M06)},
MRNUMBER = {2000g:65004},
MRREVR = {Marianne Huebner},
ANNOTE = {The stability condition described here can be
weakened to $\nu(1- 2 \theta)< \half$},
URL = {http://www.maths.man.ac.uk/~shardlow/papers/nspde1999.ps.gz}
}
@ARTICLE{shardlow:2003,
AUTHOR = {Shardlow, Tony},
TITLE = {Weak convergence of a numerical method for a stochastic heat equation},
ABSTRACT = {Weak convergence with respect to a space of twice continuously differentiable test functions is established for a discretisation of a heat equation with homogeneous Dirichlet boundary conditions in one dimension, forced by a space-time Brownian motion. The discretisation is based on finite differences in space and time, incorporating a spectral approximation in space to the Brownian motion.},
YEAR = 2003,
JOURNAL = {BIT},
PAGES = { 179--193},
VOLUME = 43,
NUMBER = 1,
URL = {http://www.springerlink.com/link.asp?id=x19h3682323xu0r6}
}
@ARTICLE{shardlow05:_weak,
AUTHOR = {Buckwar, Evelyn and Shardlow, Tony},
ABSTRACT = {A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parametrized by its time step. Weak convergence with respect to a class of smooth test functionals is established by using the infinite-dimensional version of the Kolmogorov equation. With regularity assumptions on coefficients and initial data, the rate of convergence is shown to be proportional to the time step. Some computations are presented to demonstrate the rate of convergence.},
TITLE = {Weak approximation of stochastic delay differential
equations},
JOURNAL = {IMA J. Numerical Analysis},
VOLUME = 25,
NUMBER = 1,
PAGES = {57--86},
YEAR = 2005,
URL = {http://imanum.oupjournals.org/cgi/reprint/25/1/57}
}
@MASTERSTHESIS{shardlow:93,
AUTHOR = {Shardlow, Tony},
TITLE = {The {Toda} lattice and its spectral curves},
SCHOOL = {Bath University},
YEAR = {1993},
OPTCROSSREF = {},
OPTKEY = {},
OPTADDRESS = {},
OPTMONTH = {},
NOTE = {Advisor: F. E. Burstall},
OPTTYPE = {},
OPTANNOTE = {}
}
@PHDTHESIS{shardlow:97,
AUTHOR = {Shardlow, Tony},
TITLE = {Topics in Dissipative Evolution Equations},
SCHOOL = {Stanford University},
YEAR = {1997},
OPTCROSSREF = {},
OPTKEY = {},
OPTADDRESS = {},
OPTMONTH = {},
OPTTYPE = {},
NOTE = {Advisor: A. M. Stuart},
OPTANNOTE = {}
}
@ARTICLE{shardlow:99,
AUTHOR = {Shardlow, Tony},
TITLE = {Geometric ergodicity for stochastic {PDE}s},
JOURNAL = {Stoch. Anal. App.},
YEAR = 1999,
VOLUME = 17,
PAGES = {14 pages},
NUMBER = 5,
MONTH = {September}
}
@ARTICLE{aczon:1997,
AUTHOR = {Aczon, Melissa and Gander, Martin and Gerritsen,
Margot and Shardlow, Tony and Sircar, Ronnie},
TITLE = {{SCCM Advice}: {Stanford University}'s consulting
group for applied math and numerical analysis},
JOURNAL = { IEEE Computer Science \& Engineering},
YEAR = 1997,
VOLUME = 4,
PAGES = {7--9},
NUMBER = 1
}
This file has been generated by bibtex2html 1.75