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2020

From weakly interacting particles to a regularised Dean–Kawasaki model

Cornalba, F., Shardlow, T. & Zimmer, J., 10 Jan 2020, In : Nonlinearity. 33, 2, p. 864-891 28 p.

Research output: Contribution to journalArticle

2019

A regularised Dean-Kawasaki model: derivation and analysis

Cornalba, F., Shardlow, T. & Zimmer, J., 9 Apr 2019, In : Siam Journal on Mathematical Analysis. 51, 2, p. 1137-1187 51 p.

Research output: Contribution to journalArticle

Open Access
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3 Citations (Scopus)
36 Downloads (Pure)

A walk outside spheres for the fractional Laplacian: fields and first eigenvalue

Shardlow, T., 14 Mar 2019, In : Mathematics of Computation (MCOM). 88, 320, p. 2767-2792 26 p.

Research output: Contribution to journalArticle

Open Access
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14 Downloads (Pure)
2018

Multilevel Monte Carlo and Improved Timestepping Methods in Atmospheric Dispersion Modelling

Katsiolides, G., Müller, E. H., Scheichl, R., Shardlow, T., Giles, M. B. & Thomson, D. J., 1 Feb 2018, In : Journal of Computational Physics. 354, p. 320-343 24 p.

Research output: Contribution to journalArticle

Open Access
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3 Citations (Scopus)
27 Downloads (Pure)

Unbiased `walk-on-spheres' Monte Carlo methods for the fractional Laplacian

Kyprianou, A., Osojnik, A. & Shardlow, T., 1 Jul 2018, In : IMA Journal of Numerical Analysis. 38, 3, p. 1550-1578 29 p.

Research output: Contribution to journalArticle

Open Access
7 Citations (Scopus)
2017

Gauss-quadrature method for one-dimensional mean-field SDEs

Kloeden, P. & Shardlow, T., 6 Dec 2017, In : SIAM Journal on Scientific Computing. 39, 6, p. A2784–A2807 23 p.

Research output: Contribution to journalArticle

Open Access
1 Citation (Scopus)

Langevin equations for landmark image registration with uncertainty

Shardlow, T. & Marsland, S., 31 Dec 2017, In : SIAM Journal on Imaging Sciences. 10, 2, p. 782-807 26 p.

Research output: Contribution to journalArticle

Open Access
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8 Citations (Scopus)
101 Downloads (Pure)
2016

On the pathwise approximation of stochastic differential equations

Shardlow, T. & Taylor, P., Sep 2016, In : BIT Numerical Mathematics. 56, 3, p. 1101-1129

Research output: Contribution to journalArticle

Open Access
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4 Citations (Scopus)
118 Downloads (Pure)
2015
Open Access
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2 Citations (Scopus)
134 Downloads (Pure)

Use of fin equation to calculate Nusselt numbers for rotating disks

Tang, H., Shardlow, T. & Owen, J. M., 1 Dec 2015, In : Journal of Turbomachinery: Transactions of the ASME. 137, 12, p. 1-10 10 p., 121003.

Research output: Contribution to journalArticle

Open Access
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7 Citations (Scopus)
12 Downloads (Pure)
2014

Improved simulation techniques for first exit time of neural diffusion models

Alzubaidi, H. & Shardlow, T., 2014, In : Communications in Statistics - Simulation and Computation. 43, 10, p. 2508-2520 13 p.

Research output: Contribution to journalArticle

Open Access
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3 Citations (Scopus)
128 Downloads (Pure)
2013

Interaction of waves in a one dimensional stochastic PDE model of excitable media

Alzubaidi, H. & Shardlow, T., Sep 2013, In : Discrete and Continuous Dynamical Systems - Series B. 18, 7, p. 1735-1754

Research output: Contribution to journalArticle

2012

The Milstein scheme for stochastic delay differential equations without using anticipative calculus

Shardlow, T. & Kloeden, P., 2012, In : Stochastic Analysis and Applications. 30, 2, p. 181-202 21 p.

Research output: Contribution to journalArticle

Open Access
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25 Citations (Scopus)
133 Downloads (Pure)
2011

The exponential integrator scheme for stochastic partial differential equations: pathwise error bounds

Kloeden, P., Lord, G., Neuenkirch, A. & Shardlow, T., 1 Jan 2011, In : Journal of Computational and Applied Mathematics. 235, 5, p. 1245–1260 16 p.

Research output: Contribution to journalArticle

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39 Citations (Scopus)
120 Downloads (Pure)
2008

Analysis of the geodesic interpolating spline

Shardlow, T. & Mills, A., Oct 2008, In : European Journal of Applied Mathematics. 19, 5, p. 519-539 31 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
114 Downloads (Pure)

Weak convergence of the Euler scheme for stochastic differential delay equations

Buckwar, E., Kuske, R., Mohammed, S-E. & Shardlow, T., 7 May 2008, In : London Mathematical Society Journal of Computation and Mathematics. 11, p. 60-99 39 p.

Research output: Contribution to journalArticle

2007

Postprocessing for stochastic parabolic partial differential equations

Shardlow, T. & Lord, G., 30 Apr 2007, In : SIAM Journal on Numerical Analysis (SINUM). 45, 2, p. 870-889 20 p.

Research output: Contribution to journalArticle

Open Access
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22 Citations (Scopus)
22 Downloads (Pure)

SDELab: a package for solving stochastic differential equations in MATLAB

Gilsing, H. & Shardlow, T., 15 Aug 2007, In : Journal of Computational and Applied Mathematics. 205, 2, p. 1002-1018 17 p.

Research output: Contribution to journalArticle

Open Access
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24 Citations (Scopus)
31 Downloads (Pure)
2006

Geometric ergodicity for dissipative particle dynamics

Shardlow, T. & Yan, Y., 2006, In : Stochastics and Dynamics. 6, 1, p. 123-154

Research output: Contribution to journalArticle

File
14 Citations (Scopus)
26 Downloads (Pure)

Modified equations for stochastic differential equations

Shardlow, T., 31 Mar 2006, In : BIT Numerical Mathematics. 46, 1, p. 111-125 15 p.

Research output: Contribution to journalArticle

Open Access
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19 Citations (Scopus)
23 Downloads (Pure)
2005

Numerical simulation of stochastic PDEs for excitable media

Shardlow, T., 15 Mar 2005, In : Journal of Computational and Applied Mathematics. 175, 2, p. 429-446 18 p.

Research output: Contribution to journalArticle

41 Citations (Scopus)

Weak approximation of stochastic differential delay equations

Buckwar, E. & Shardlow, T., 1 Jan 2005, In : IMA Journal of Numerical Analysis. 25, 1, p. 57-86 30 p.

Research output: Contribution to journalArticle

17 Citations (Scopus)
2004

Nucleation of waves in excitable media by noise

Shardlow, T., 31 Dec 2004, In : Multiscale Modeling and Simulation : A SIAM Interdisciplinary Journal. 3, 1, p. 151-167 17 p.

Research output: Contribution to journalArticle

Open Access
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7 Citations (Scopus)
21 Downloads (Pure)
2003

Splitting for dissipative particle dynamics

Shardlow, T., 31 Dec 2003, In : SIAM Journal on Scientific Computing. 24, 4, p. 1267-1282 16 p.

Research output: Contribution to journalArticle

Open Access
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96 Citations (Scopus)
20 Downloads (Pure)

Weak convergence of a numerical method for a stochastic heat equation

Shardlow, T., 2003, In : BIT Numerical Mathematics. 43, 1, p. 179-193

Research output: Contribution to journalArticle

28 Citations (Scopus)
2002

A coupled Cahn–Hilliard particle system

Shardlow, T., 13 Aug 2002, In : Electronic Journal of Differential Equations. 2002, 73, p. 1-21 21 p.

Research output: Contribution to journalArticle

Open Access
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21 Downloads (Pure)
2000

A perturbation theory for ergodic properties of Markov chains

Shardlow, T. & Stuart, A., 1 Jan 2000, In : SIAM Journal on Numerical Analysis (SINUM). 37, 4, p. 1120-1137 18 p.

Research output: Contribution to journalArticle

Open Access
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31 Citations (Scopus)
20 Downloads (Pure)

Stochastic perturbations of the Allen-Cahn equation

Shardlow, T., 1 Dec 2000, In : Electronic Journal of Differential Equations. 2000, 47, p. 1-19 19 p.

Research output: Contribution to journalArticle

Open Access
8 Citations (Scopus)
1999

Geometric ergodicity for stochastic PDEs

Shardlow, T., 1 Jan 1999, In : Stochastic Analysis and Applications. 17, 5, p. 857-869 13 p.

Research output: Contribution to journalArticle

6 Citations (Scopus)

Numerical methods for stochastic parabolic PDEs

Shardlow, T., 1999, In : Numerical Functional Analysis and Optimization. 20, 1-2, p. 121-145

Research output: Contribution to journalArticle

74 Citations (Scopus)
1997

Inertial manifolds and linear multistep methods

Shardlow, T., 30 Apr 1997, In : Numerical Algorithms. 14, 1-3, p. 189-209 21 p.

Research output: Contribution to journalArticle

File
4 Citations (Scopus)
24 Downloads (Pure)
1996

Periodic orbits and unstable manifolds

Shardlow, T., 1 Jan 1996, In : Numerical Functional Analysis and Optimization. 17, 9-10, p. 963-989

Research output: Contribution to journalArticle

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20 Downloads (Pure)
1994

The multiplicity of bifurcation for area-preserving mappings

Shardlow, T., 1 Jul 1994, In : Bulletin of the London Mathematical Society. 26, 4, p. 382-394

Research output: Contribution to journalArticle