MacKay, R.S. & Shardlow, T. (1994) The multiplicity of bifurcation for
area-preserving mappings. Bulletin of the London Mathematics Society, 4, 382–394.
bib
@article{mackay:94,
author = {MacKay, Robert S. and Shardlow, Tony},
title = {The multiplicity of bifurcation for
area-preserving mappings},
journal = {Bulletin of the London Mathematics Society},
year = {1994},
volume = {4},
pages = {382--394},
doi = {10.1112/blms/26.4.382},
file = {R1.pdf}
}
Shardlow, T. (1996) Periodic orbits and unstable manifolds. Numerical Functional Analysis and Optimization, 17, 963–989.
bib
@article{shardlow:1996,
author = {Shardlow, Tony},
title = {Periodic orbits and unstable manifolds},
journal = {Numerical Functional Analysis and Optimization},
year = {1996},
doi = {10.1080/01630569608816737},
volume = {17},
number = {9--10},
pages = {963--989},
file = {R2.pdf}
}
Shardlow, T. (1997) Inertial manifolds and linear multistep
methods. Numerical Algorithms, 14, 189–209.
bib
@article{shardlow:1997,
author = {Shardlow, Tony},
title = {Inertial manifolds and linear multistep
methods},
journal = {Numerical Algorithms},
year = {1997},
volume = {14},
number = {1--3},
pages = {189--209},
doi = {10.1023/A:1019165014068},
file = {R3.pdf}
}
Aczon, M., Gander, M., Gerritsen, M., Shardlow, T., & Sircar, R. (1997) SCCM Advice: Stanford University’s
consulting group for applied math and numerical
analysis. IEEE Computer Science & Engineering, 4, 7–9.
bib
@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},
doi = {10.1109/99.590850},
file = {R4.pdf}
}
Shardlow, T. (1999) Numerical methods for stochastic parabolic
PDEs. Numerical Functional Analysis and Optimization, 20, 121–145.
bib
@article{shardlow:1999a,
author = {Shardlow, Tony},
title = {Numerical methods for stochastic parabolic
{P}{D}{E}s},
journal = {Numerical Functional Analysis and Optimization},
volume = {20},
year = {1999},
doi = {10.1080/01630569908816884},
number = {1-2},
pages = {121--145},
issn = {0163-0563},
coden = {NFADOL},
annote = {The stability condition described here can be
weakened to $\nu(1- 2 \theta)< \half$},
file = {R5.pdf}
}
Shardlow, T. (1999) Geometric ergodicity for stochastic PDEs. Stochastic Analysis and Applications, 17, 14 pages.
bib
@article{shardlow:99,
author = {Shardlow, Tony},
title = {Geometric ergodicity for stochastic {PDE}s},
journal = {Stochastic Analysis and Applications},
year = {1999},
volume = {17},
pages = {14 pages},
doi = {10.1080/07362999908809639},
number = {5},
file = {R6.pdf}
}
Shardlow, T. & Stuart, A.M. (2000) A perturbation theory for ergodic properties of
Markov chains. SIAM Journal on Numerical Analysis, 37, 1120–1137.
bib
@article{shardlow00:_pertur_theor,
author = {Shardlow, Tony and Stuart, Andrew M.},
title = {A perturbation theory for ergodic properties of
{Markov} chains},
journal = {SIAM Journal on Numerical Analysis},
year = {2000},
volume = {37},
number = {4},
pages = {1120--1137},
doi = {10.1137/S0036142998337235},
file = {R7.pdf}
}
Shardlow, T. (2000) Stochastic perturbations of the Allen–Cahn
equation. Electronic Journal of Differential Equations, 47, 19 pages.
bib
@article{shardlow00:_stoch_allen_cahn,
author = {Shardlow, Tony},
title = {Stochastic perturbations of the {A}llen--{C}ahn
equation},
journal = {Electronic Journal of Differential Equations},
year = {2000},
volume = {47},
pages = {19 pages},
issn = {1072-6691},
file = {R8.pdf}
}
Shardlow, T. (2002) A coupled Cahn–Hilliard particle system. Electronic Journal of Differential Equations, 73, 21 pages .
bib
@article{shardlow02:_cahn_hilliar,
author = {Shardlow, Tony},
title = {A coupled {C}ahn--{H}illiard particle system},
journal = {Electronic Journal of Differential Equations},
year = {2002},
pages = {21 pages },
volume = {73},
issn = {1072-6691},
file = {R9.pdf}
}
Shardlow, T. (2003) Splitting for dissipative particle dynamics. SIAM Journal on Scientific Computing, 24, 1267–1282.
bib
@article{shardlow03:_split,
author = {Shardlow, Tony},
title = {Splitting for dissipative particle dynamics},
journal = {SIAM Journal on Scientific Computing},
volume = {24},
year = {2003},
number = {4},
pages = {1267--1282},
issn = {1095-7197},
doi = {10.1137/S1064827501392879},
file = {R11.pdf}
}
Shardlow, T. (2003) Weak convergence of a numerical method for a
stochastic heat equation. BIT Numerical Mathematics, 43, 179–193.
bib
@article{shardlow:2003,
author = {Shardlow, Tony},
title = {Weak convergence of a numerical method for a
stochastic heat equation},
year = {2003},
journal = {BIT Numerical Mathematics},
pages = { 179--193},
doi = {10.1023/A:1023661308243},
volume = {43},
number = {1},
file = {R10.pdf}
}
Shardlow, T. (2004) Nucleation of waves in excitable media by
noise. SIAM Multiscale modelling and simulation, 3, 151–167.
bib
@article{shardlow04:_nucleat_pde,
author = {Shardlow, Tony},
title = {Nucleation of waves in excitable media by
noise},
journal = {SIAM Multiscale modelling and simulation},
volume = {3},
number = {1},
doi = {10.1137/030602149},
pages = {151--167},
year = {2004},
file = {R12.pdf}
}
Shardlow, T. (2005) Numerical simulation of stochastic PDEs for
excitable media. Journal of Computational and Applied Mathematics, 175, 429–446.
bib
@article{shardlow05:_numer_pdes,
author = {Shardlow, Tony},
title = {Numerical simulation of stochastic {PDE}s for
excitable media},
journal = {Journal of Computational and Applied Mathematics},
volume = {175},
number = {2},
month = mar,
pages = {429--446},
year = {2005},
doi = {10.1016/j.cam.2004.06.020},
file = {R13.pdf}
}
Buckwar, E. & Shardlow, T. (2005) Weak approximation of stochastic delay
differential equations. IMA Journal of Numerical Analysis, 25, 57–86.
bib
@article{shardlow05:_weak,
author = {Buckwar, Evelyn and Shardlow, Tony},
title = {Weak approximation of stochastic delay
differential equations},
journal = {IMA Journal of Numerical Analysis},
volume = {25},
doi = {10.1093/imanum/drh012},
number = {1},
pages = {57-86},
year = {2005},
file = {R14.pdf}
}
Shardlow, T. (2006) Modified equations for stochastic differential
equations. BIT Numerical Mathematics, 46, 111–125.
bib
@article{shardlow04:_modif_equat,
author = {Shardlow, Tony},
title = {Modified equations for stochastic differential
equations},
year = {2006},
journal = {BIT Numerical Mathematics},
volume = {46},
pages = {111-125},
doi = {10.1007/s10543-005-0041-0},
file = {R16.pdf}
}
Shardlow, T. & Yan, Y. (2006) Geometric ergodicity for dissipative particle
dynamics. Stochastics and Dynamics, 6, 31 pages.
bib
@article{shardlow04:_geomet,
author = {Shardlow, Tony and Yan, Yubin},
title = {Geometric ergodicity for dissipative particle
dynamics},
journal = {Stochastics and Dynamics},
volume = {6},
number = {1},
doi = {10.1142/S0219493706001670},
pages = {31 pages},
year = {2006},
file = {R15.pdf}
}
Mills, A., Marsland, S., & Shardlow, T. (2006) Computing the geodesic interpolating spline. Biomedical Image Registration, Lecture Notes in Computer Science, 4057, 169–177.
bib
@article{mills06:_comput,
author = {Mills, Anna and Marsland, Stephen and Shardlow, Tony},
title = {Computing the geodesic interpolating spline},
booktitle = {Biomedical Image Registration},
pages = {169--177},
publisher = {Springer},
doi = {10.1007/11784012_21},
year = {2006},
editor = {Pluim, J. P. W. and Lika, B. and Gerritsen, F. A.},
volume = {4057},
series = {Lecture Notes in Computer Science},
file = {R17.pdf}
}
Gilsing, H. & Shardlow, T. (2007) SDELab: a package for solving stochastic
differential equations in MATLAB. Journal of Computational and Applied
Mathematics, 205, 1002–1018.
bib
@article{gilsing05:_sdelab_matlab,
author = {Gilsing, Hagen and Shardlow, Tony},
title = {S{DEL}ab: a package for solving stochastic
differential equations in {MATLAB}},
journal = {Journal of Computational and Applied
Mathematics},
volume = {205},
year = {2007},
number = {2},
pages = {1002--1018},
doi = {10.1016/j.cam.2006.05.037},
issn = {0377-0427},
coden = {JCAMDI},
addendum = {The original MATLAB implementation is no longer available. A Julia implementation is available on Github},
github = {tonyshardlow/SDELAB2},
file = {R19.pdf}
}
Lord, G.J. & Shardlow, T. (2007) Postprocessing for stochastic parabolic partial
differential equations. SIAM Journal on Numerical Analysis, 45, 870–889.
bib
@article{shardlow07,
author = {Lord, Gabriel J. and Shardlow, Tony},
title = {Postprocessing for stochastic parabolic partial
differential equations},
journal = {SIAM Journal on Numerical Analysis},
volume = {45},
year = {2007},
number = {2},
pages = {870--889},
issn = {0036-1429},
doi = {10.1137/050640138},
file = {R18.pdf}
}
Mills, A. & Shardlow, T. (2008) Analysis of the geodesic interpolating spline. European Journal of Applied Mathematics, 19, 519–539.
bib
@article{shardlow08:gis,
author = {Mills, Anna and Shardlow, Tony},
title = {Analysis of the geodesic interpolating spline},
journal = {European Journal of Applied Mathematics},
volume = {19},
year = {2008},
number = {5},
doi = {10.1017/S0956792508007493},
pages = {519--539},
file = {R20.pdf}
}
Buckwar, E., Kuske, R., Mohammed, S.-E., & Shardlow, T. (2008) Weak convergence of the Euler scheme for
stochastic differential delay equations. LMS Journal of Computation and Mathematics, 11, 60–99.
bib
@article{shardlow08:delay,
author = {Buckwar, Evelyn and Kuske, Rachel and Mohammed, Salah-Eldin and Shardlow, Tony},
title = {Weak convergence of the {E}uler scheme for
stochastic differential delay equations},
journal = { LMS Journal of Computation and Mathematics},
volume = {11},
year = {2008},
pages = {60--99},
doi = {10.1112/S146115700000053X},
file = {R21.pdf}
}
Alzubaidi, H. & Shardlow, T. (2009) Numerical simulations of SDEs and SPDEs. Stochastic Methods in Neuroscience, 344–366.
bib
@article{shardlow09:hasan,
author = {Alzubaidi, Hasan and Shardlow, Tony},
editor = {Laing, Carlo and Lord, Gabriel},
booktitle = {Stochastic Methods in Neuroscience},
title = {Numerical simulations of {SDE}s and {SPDE}s},
chapter = {12},
pages = {344-366},
publisher = {OUP},
year = {2009},
doi = {10.1093/acprof:oso/9780199235070.003.0012}
}
Kloeden, P.E., Lord, G., Neuenkirch, A., & Shardlow, T. (2011) The exponential integrator scheme for
stochastic partial differential equations:
pathwise error bounds. Journal of Computational and Applied Mathematics, 235, 1245–1260.
bib
@article{shardlow08:andreas,
author = {Kloeden, Peter E. and Lord, Gabriel and Neuenkirch, Andreas and Shardlow, Tony},
title = {The exponential integrator scheme for
stochastic partial differential equations:
pathwise error bounds},
journal = {Journal of Computational and Applied Mathematics},
volume = {235},
number = {5},
doi = {10.1016/j.cam.2010.08.011},
year = {2011},
pages = {1245--1260},
file = {R23.pdf}
}
Kloeden, P.E. & Shardlow, T. (2012) The Milstein scheme for stochastic delay
differential equations without using
anticipative calculus. Stochastic Analysis and Applications, 30, 181–202.
bib
@article{kloeden10:milstein_delay,
author = {Kloeden, Peter E. and Shardlow, Tony},
title = {The {Milstein} scheme for stochastic delay
differential equations without using
anticipative calculus},
journal = {Stochastic Analysis and Applications},
year = {2012},
doi = {10.1080/07362994.2012.628907},
volume = {30},
number = {2},
pages = {181--202},
file = {R24.pdf}
}
Alzubaidi, H. & Shardlow, T. (2013) Interaction of waves in a one-dimensional
stochastic PDE model of excitable media. Discrete and Continuous Dynamical
Systems – Series B, 18, 1735–1754.
bib
@article{alzubaidi13:_inter_pde,
author = {Alzubaidi, Hasan and Shardlow, Tony},
title = {Interaction of waves in a one-dimensional
stochastic {PDE} model of excitable media},
journal = {Discrete and Continuous Dynamical
Systems -- Series B},
year = {2013},
volume = {18},
number = {7},
pages = {1735--1754},
doi = {10.3934/dcdsb.2013.18.1735},
file = {R25.pdf}
}
Alzubaidi, H. & Shardlow, T. (2014) Improved simulation techniques for first exit
time of neural diffusion models. Communications in Statistics – Simulation
and Computation, 43.
bib
@article{alzubaidi,
author = {Alzubaidi, Hasan and Shardlow, Tony},
title = {Improved simulation techniques for first exit
time of neural diffusion models},
journal = {Communications in Statistics -- Simulation
and Computation},
volume = {43},
number = {10},
year = {2014},
doi = {10.1080/03610918.2012.755197},
file = {R26.pdf}
}
Tang, H., Shardlow, T., & Owen, J.M. (2015) Use of fin equation to calculate Nusselt
numbers for rotating discs. J. Turbomach, 137.
bib
@article{huimike,
author = {Tang, Hui and Shardlow, Tony and Owen, J. Michael},
title = {Use of fin equation to calculate {Nusselt}
numbers for rotating discs},
journal = {J. Turbomach},
year = {2015},
volume = {137},
number = {12},
doi = {10.1115/1.4031355},
file = {R27.pdf}
}
Müller, E., Scheichl, R., & Shardlow, T. (2015) Improving MLMC for SDEs with application to the
Langevin equation. Proceedings of the Royal Society A, 471.
bib
@article{eikerob2,
author = {M\"uller, Eike and Scheichl, Rob and Shardlow, Tony},
title = {Improving {MLMC} for {SDEs} with application to the
{Langevin} equation},
journal = {Proceedings of the Royal Society A},
volume = {471},
number = {20140679},
doi = {10.1098/rspa.2014.0679},
year = {2015},
eprinttype = {arxiv},
eprint = {1409.2342},
file = {R28.pdf},
bitbucket = em459/mlmclangevin
}
Shardlow, T. & Taylor, P. (2016) On the pathwise approximation
of stochastic differential equations. BIT Numerical Mathematics, 56, 1101–1129.
bib
@article{philip2,
author = {Shardlow, Tony and Taylor, Phillip},
title = {On the pathwise approximation
of stochastic differential equations},
journal = {BIT Numerical Mathematics},
volume = {56},
issue = {3},
pages = {1101--1129},
year = {2016},
doi = {10.1007/s10543-015-0597-2},
eprinttype = {arxiv},
eprint = {1409.2362},
file = {R29.pdf}
}
Kloeden, P. & Shardlow, T. (2017) Gauss-quadrature method for one-dimensional mean-field SDEs. SIAM Journal on Scientific Computing, 39, A2784–A2807.
bib
@article{gqpeter,
author = {Kloeden, Peter and Shardlow, Tony},
title = {Gauss-quadrature method for one-dimensional mean-field SDEs},
journal = {SIAM Journal on Scientific Computing},
year = {2017},
volume = {39},
number = {6},
pages = {A2784--A2807},
doi = {10.1137/16M1095688},
eprinttype = {arxiv},
eprint = {1608.06741},
file = {R32.pdf},
github = tonyshardlow/sdelab2
}
Marsland, S. & Shardlow, T. (2017) Langevin equations for landmark image registration with uncertainty. SIAM Journal on Imaging Sciences, 10, 782–780.
bib
@article{reg_sde,
author = {Marsland, Stephen and Shardlow, Tony},
title = {Langevin equations for landmark image registration with uncertainty},
journal = {SIAM Journal on Imaging Sciences},
volume = {10},
number = {2},
pages = {782-80},
eprinttype = {arxiv},
eprint = {1605.09276},
gitub = {tonyshardlow/reg_sde},
year = {2017},
doi = {10.1137/16M1079282},
file = {R30.pdf},
github = tonyshardlow/reg_sde
}
Katsiolides, G., Mueller, E.H., Scheichl, R., Shardlow, T., Giles, M.B., & Thomson, D.J. (2018) Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling. Journal of Computational Physics, 354, 320–343.
bib
@article{1612.07717,
author = {Katsiolides, Grigoris and Mueller, Eike H. and Scheichl, Robert and Shardlow, Tony and Giles, Michael B. and Thomson, David J.},
title = {Multilevel {Monte Carlo} and Improved Timestepping Methods in Atmospheric Dispersion Modelling},
journal = {Journal of Computational Physics},
doi = {10.1016/j.jcp.2017.10.035},
year = {2018},
volume = {354},
pages = {320--343},
eprinttype = {arxiv},
eprint = {1612.07717},
file = {R33.pdf},
bitbucket = em459/mlmclangevin
}
Kyprianou, A., Osojnik, A., & Shardlow, T. (2018) Unbiased walk-on-spheres Monte Carlo methods
for the fractional Laplacian. IMA Journal of Numerical Analysis, 38.
bib
@article{wos,
author = {Kyprianou, A. and Osojnik, A. and Shardlow, Tony},
title = {Unbiased walk-on-spheres {Monte Carlo} methods
for the fractional {Laplacian}},
journal = {IMA Journal of Numerical Analysis},
eprinttype = {arxiv},
eprint = {1609.03127},
doi = {10.1093/imanum/drx042},
volume = {38},
number = {3},
year = {2018},
file = {R31.pdf},
bitbucket = wos_paper/wos_repo
}
Cornalba, F., Shardlow, T., & Zimmer, J. (2019) Regularised Dean–Kawasaki model: derivation and analysis. SIAM Journal on Mathematical Analysis, 51, 1137–1187.
bib
@article{federico2018,
author = {Cornalba, Federico and Shardlow, Tony and Zimmer, Johannes},
title = {Regularised {Dean}--{Kawasaki} model: derivation and analysis},
journal = {SIAM Journal on Mathematical Analysis},
doi = {10.1137/18M1172697},
volume = {51},
number = {2},
pages = {1137--1187},
eprinttype = {arxiv},
eprint = {1802.01716},
year = {2019},
month = apr,
file = {R35.pdf}
}
Shardlow, T. (2019) A walk outside spheres for the fractional Laplacian: fields and first eigenvalue. Mathematics of Computation, 88, 2767–2792.
bib
@article{field_wos,
author = {Shardlow, Tony},
title = {A walk outside spheres for the fractional Laplacian: fields and first eigenvalue},
journal = {Mathematics of Computation},
year = {2019},
doi = {10.1090/mcom/3422},
volume = {88},
pages = {2767-2792},
file = {R34.pdf},
eprinttype = {arxiv},
eprint = {1803.03921},
github = {tonyshardlow/julia_wos}
}
Cornalba, F., Shardlow, T., & Zimmer, J. (2020) From weakly interacting particles to a regularised Dean–Kawasaki model. Nonlinearity, 33, 864–891.
bib
@article{federico2018b,
author = {Cornalba, Federico and Shardlow, Tony and Zimmer, Johannes},
title = {From weakly interacting particles to a regularised {Dean}--{Kawasaki} model},
journal = {Nonlinearity},
eprinttype = {arxiv},
eprint = {1811.06448},
year = {2020},
volume = {33},
number = {2},
pages = {864--891},
month = jan,
doi = {10.1088/1361-6544/ab5174},
file = {R36.pdf}
}
Cornalba, F., Shardlow, T., & Zimmer, J. (2021) Well-posedness for a regularised inertial Dean-Kawasaki model for slender particles in several space dimensions. Journal of Differential Equations, 284, 253–283.
bib
@article{2005.06014,
author = {Cornalba, Federico and Shardlow, Tony and Zimmer, Johannes},
title = {Well-posedness for a regularised inertial {Dean-Kawasaki} model for slender particles in several space dimensions},
year = {2021},
volume = {284},
month = may,
day = {25},
pages = {253--283},
file = {R37.pdf},
doi = {10.1016/j.jde.2021.02.048},
journal = {Journal of Differential Equations},
eprinttype = {arxiv},
eprint = {2005.06014}
}
Rambojun, A., Tillett, W., Shardlow, T., & Campbell, N. (2021) Active Latent Space Shape Model: A Bayesian Treatment of Shape Model Adaptation with an Application to Psoriatic Arthritis Radiographs. 2021 IEEE Winter Conference on Applications of Computer Vision (WACV).
bib
@article{adwaye:2021,
author = {Rambojun, A. and Tillett, W. and Shardlow, T. and Campbell, N.},
month = jan,
title = {Active Latent Space Shape Model: A Bayesian Treatment of Shape Model Adaptation with an Application to Psoriatic Arthritis Radiographs},
year = {2021},
journal = {2021 IEEE Winter Conference on Applications of Computer Vision (WACV)},
file = {R38.pdf}
}
Tang, H., Deveney, T., Shardlow, T., & Lock, G. (2022) Use of Bayesian Statistics to Calculate Transient Heat Fluxes on Compressor Discs. Physics of Fluids, DOI: 10.1063/5.0091371.
bib
@article{tep,
doi = {10.1063/5.0091371},
url = {https://doi.org/10.1063%2F5.0091371},
year = {2022},
month = apr,
publisher = {{AIP} Publishing},
author = {Tang, Hui and Deveney, Teo and Shardlow, Tony and Lock, Gary},
title = {Use of Bayesian Statistics to Calculate Transient Heat Fluxes on Compressor Discs},
journal = {Physics of Fluids}
}
Deveney, T., Mueller, E., & Shardlow, T. (2023) Deep surrogate accelerated delayed-acceptance Hamiltonian Monte Carlo for Bayesian inference of spatio-temporal heat fluxes in rotating disc systems. SIAM Uncertainty Quantification, DOI: 10.1137/22M1513113.
bib
@article{teo_hmc,
author = {Deveney, T. and Mueller, E. and Shardlow, T.},
title = {Deep surrogate accelerated delayed-acceptance Hamiltonian Monte Carlo for Bayesian inference of spatio-temporal heat fluxes in rotating disc systems},
eprinttype = {arxiv},
eprint = {2204.02272},
journal = {SIAM Uncertainty Quantification},
doi = {10.1137/22M1513113},
year = {2023},
vol = {11},
number = {3}
}
Cornalba, F. & Shardlow, T. (2023) The Regularised Inertial Dean-Kawasaki equation: discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis, DOI: 10.1051/m2an/2023077.
bib
@article{2207.09989,
author = {Cornalba, Federico and Shardlow, Tony},
title = {The Regularised Inertial {Dean-Kawasaki} equation: discontinuous Galerkin approximation and modelling for low-density regime},
year = {2023},
doi = {10.1051/m2an/2023077},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
eprinttype = {arxiv},
eprint = {2207.09989},
github = {tonyshardlow/RIDK-FD}
}
