# Publications

J. A. Carrillo, A. Chertock, and Y. Huang,

*A finite-volume method for nonlinear nonlocal equations with a gradient flow structure*,

submitted.

M. Castro Diaz, Y. Cheng, A. Chertock, and A. Kurganov,

*Solving two-mode shallow water equations using finite volume methods*,

submitted.

A. Chertock, S. Cui, A. Kurganov, and T. Wu,

*Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms*,

submitted.

A. Chertock, A. Kurganov and J. Miller,

*Central-upwind scheme for a non-hydrostatic Saint-Venant system*,

submitted.

A. Chertock, M. Herty and A. Kurganov,

*An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs*,

Computational Optimization and Applications, accepted.

A. Chertock, J.-G. Liu and T. Pendleton,

*Elastic collisions among peakon solutions for the Camassa-Holm equation*,

Applied Numerical
Mathematics, in press.

A. Chertock, A. Kurganov and Y. Liu,

*Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients*,

Numerische Mathematik, in press.

A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev,

*Pedestrian flow models with slowdown interactions*,

M3AS: Mathematical Models and Methods in Applied Sciences, **24** (2014), pp. 249-275.

A. Chertock, A. Kurganov, Z. Qu and T. Wu,

*On a three-layer approximation of two-layer shallow water equations*,

Mathematical Modelling and Analysis, ** 18** (2013), pp. 675-693.

A. Chertock, J.-G. Liu and T. Pendleton,

*Convergence of a particle method and global weak solutions for a family of evolutionary PDEs*,

SIAM Journal on Numerical Analysis, **50** (2012), pp. 1-21.

A. Chertock, K. Fellner, A. Kurganov, A. Lorz and P. Markowich,

*Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach*,

Journal of Fluid Mechanics, Cambridge University Press 2012, ** 694** (2012), pp. 155-190.

A. Chertock, J.-G. Liu and T. Pendleton,

*Convergence analysis of the particle method for the Camassa-Holm equation*,

Proceedings of the 13th International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications'',

(Ph. G. Ciarlet and Ta-Tsien Li, eds.), Contemporary Applied Mathematics, 2012, pp. 365-373.

A. Chertock, A. Kurganov, X. Wang and Y. Wu,

*On a chemotaxis model with saturated chemotactic flux*,

Kinetic and Related Models, **5** (2012), pp. 51-95.

A. Chertock, P. Du Toit and J. E. Marsden,

*Integration of the EPDiff equation by particle methods*,

M2AN Mathematical Modelling and Numerical Analysis,** 46** (2012), pp. 515-534.

A. Chertock, C.I. Christov and A. Kurganov,

*Central-upwind schemes for the Boussinesq paradigm equations*,

in Computational Science and High Performance Computing IV,

The 4th Russian-German Advanced Research Workshop, Freiburg, Germany,

vol. 115 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design,

Springer, 2011, pp. 267-281.

A. Chertock, C. Doering, E. Kashdan and A. Kurganov,

*A fast explicit operator splitting method for passive scalar advection*,

Journal of Scientific Computing,** 45** (2010), pp. 200-214.

A. Chertock and A. Kurganov,

*On splitting-based numerical methods for convection-diffusion equations*,

in Numerical Methods for Balance Laws, Quaderni di Matematica, Dept. Math.,

Seconda Univ. Napoli, Caserta, **24** (2009), p. 303-343.

A. Chertock, A. Kurganov and G. Petrova,

*Fast explicit operator splitting method for convection-diffusion equations*,

International Journal for Numerical Methods in Fluids, ** 59** (2009), pp. 309-332.

A. Chertock and A. Kurganov,

*Computing multivalued solutions of pressureless gas dynamics by deterministic particle
methods*,

Communications in Computational Physics, ** 5 ** (2009), pp. 565-581.

A. Chertock and A. Kurganov,

*A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models*,

Numerische Mathematik, ** 111 ** (2008), pp. 169-205.

A. Chertock, D. Gottlieb and A. Solomonoff,

*Modified optimal prediction and its application to a particle-method problem*,

Journal of Scientific Computing, ** 37** (2008), pp. 189-201.

A. Chertock and A. Kurganov,

*A simple Eulerian finite-volume method for compressible fluids in domains with moving
boundaries*,

Communications in Mathematical Sciences, ** 6 ** (2008), pp. 531-556.

A. Chertock, S. Karni and A. Kurganov,

*Interface tracking method for compressible multifluids*,

Mathematical Modelling and Numerical Analysis, M2AN, ** 42 ** (2008), pp. 991-1019.

A. Chertock, E. Kashdan and A. Kurganov,

*Propagation of diffusing pollutant by a hybrid Eulerian-Lagrangian method*,

Hyperbolic Problems: Theory, Numerics, Applications (Lyon 2006), pp. 371-380, Springer, 2008.

A. Chertock, A. Kurganov and Yu. Rykov,

*A new sticky particle method for pressureless gas dynamics*,

SIAM Journal on Numerical Analysis, ** 45 ** (2007), pp. 2408-2441.

A. Chertock, A. Kurganov and G. Petrova,

*Finite-volume-particle methods for models of transport of pollutant in shallow water*,

Journal of Scientific Computing, ** 27 ** (2006), pp. 189-199.

A. Chertock, A. Kurganov,

*On a practical implementation of particle methods*,

Applied Numerical Mathematics, ** 56** (2006), pp. 1418-1431.

A. Chertock, A. Kurganov and G. Petrova,

*Fast explicit operator splitting method. Application to the polymer system*,

Finite Volumes for Complex Applications IV (2005), pp. 63-72.

A. Chertock, A. Kurganov,

*Conservative locally moving mesh method for multifluid flows*,

Finite Volumes for Complex Applications IV (2005), pp. 273-284.

A. Chertock, A. Kurganov and P. Rosenau,

*On degenerate saturated-diffussion equations with convection*,

Nonlinearity, ** 18** (2005), pp. 609-630.

A. Chertock, A. Kurganov,

*On a hybrid final-volume-particle method*,

Mathematical Modelling and Numerical Analysis,** 38** (2004), pp. 1071--1091.

A. Chertock, D. Levy,

*On wavelet-based numerical homogenization*,

SIAM Journal of Multiscale Modeling and Simulation, ** 3** (2004), pp. 65-88.

A. Chertock, A. Kurganov and P. Rosenau,

*Formation of discontinuities in flux-saturated degenerate parabolic equations*,

Nonlinearity ** 16 ** (2003), pp. 1875-1898.

A. Chertock, D. Levy,

*Particle methods for the KdV equation*,

Journal of Scientific Computing, ** 17 ** (2002), pp. 491-499.

A. Chertock,

*On the stability of a class of self-similar solutions for the filtration-absorption equation*,

European Journal of Applied Mathematics, ** 13** (2002), pp. 179-194.

A. Chertock, D. Levy,

*Particle methods for dispersive equations*,

Journal of Computational Physics,** 171** (2001), pp. 708-730.

G.I.Barenblatt, M. Bertsch, A. Chertock and V.M. Prostokishin,

*Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation*,

Proceedings of National Academy of Sciences, USA, **97** (2000), pp. 9844-9848.

S. Abarbanel, A Chertock and A. Yefet,

*Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for
hyperbolic PDEs, II*,

Journal of Computational Physics, **160** (2000), pp. 67-87.

S. Abarbanel, A. Chertock,

*Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for
hyperbolic PDEs, I*,

Journal of Computational Physics, **160** (2000), pp. 42-66.

A. Chertock,

*Strict stability of high-order compact implicit finite-difference schemes: the role of boundary conditions for
hyperbolic PDEs*,

PhD Thesis, Tel-Aviv University, Tel-Aviv, Israel ,1999.