Publications

 

Publications

A. Chertock, A. Kurganov, M. Ricchiuto and T. Wu,
Adaptive moving mesh upwind scheme for the two-species chemotaxis model,
submitted.

X. Liu, A. Chertock, and A. Kurganov,
An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces,
submitted.

A. Chertock, P. Degond, S. Hecht, and J.-P. Vincent,
Incompressible limit of a continuum model of tissue growth with segregation for two cell populations,
submitted.

Y. Cheng, A. Chertock, M. Herty and A. Kurganov,
A new approach for designing moving-water equilibria preserving schemes for the shallow water equations,
submitted.

A. Chertock, S. Jin and A. Kurganov,
A well-balanced operator splitting based stochastic Galerkin method for the one-dimensional Saint-Venant system with uncertainty,
submitted.

A. Chertock, S. Jin and A. Kurganov,
An operator splitting based stochastic Galerkin method for the one-dimensional compressible Euler equations with uncertainty,
submitted.

A. Chertock, A. Kurganov and J. Miller,
Central-upwind scheme for a non-hydrostatic Saint-Venant system,
submitted.

A. Chertock, A. Kurganov, M. Lukacova-Medvidova, and S. Ozcan,
An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions,
Kinetic and Related Models, (2019), to appear.

A. Chertock, M. Herty and S. Ozcan,
Well-balanced central-upwind schemes for 2×2 systems of balance laws,
Proceedings of the XVI International Conference on Hyperbolic Problems, Springer, (2018), to appear.

A. Chertock, S. Cui, A. Kurganov, S. Ozcan and E Tadmor,
Well-balanced central-upwind schemes for the Euler equations with gravitation,
Journal of Computational Physics, 358 (2018), pp. 36-52.

A. Chertock, C. Tan and B. Yan,
An asymptotic preserving scheme for kinetic models with singular limit,
Kinetic and Related Models, 11 (2018), pp. 735-756.

A. Chertock, M. Dudzinski, A. Kurganov and M. Lukacova-Medvidova,
Well-balanced schemes for the shallow water equations with Coriolis forces,
Numerische Mathematik, 138 (2018), pp. 939-973.

A. Chertock, Y. Epshteyn, H. Hu and A. Kurganov,
High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems,
Advances in Computational Mathematics, 44 (2018), pp. 327-350.

A. Chertock, A. Coco, A. Kurganov and G. Russo,
A second-order finite-difference method for compressible fluids in domains with moving boundaries,
Communications in Computational Physics, 23 (2018), pp. 230-263.

Y. Cheng, A. Chertock, and A. Kurganov,
A simple finite-volume method on a cartesian mesh for pedestrian flows with obstacles,
Finite Volumes for Complex Applications, VIII—methods and theoretical aspects (Lille, 2017),
pp. 43-55, Springer Proc. Math. Stat., 199, 2017.

A. Chertock, S. Cui and A. Kurganov,
Hybrid finite-volume-particle methods for dusty gas flows ,
SMAI Journal of Computational Mathematics 3 (2017), pp. 139-180.

A. Chertock,
A practical guide to deterministic particle methods,
Handbook of Numerical Methods for Hyperbolic Problems, Volume 18, 1st Edition, Elsevier, (2017), pp. 177-202.

A. Chertock, P. Degond and J. Neusser,
An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations ,
Journal of Computational Physics, 335 (2017), pp. 387-403.

A. Bernstein, A. Chertock and A. Kurganov,
Central-upwind scheme for shallow water equations with discontinuous bottom topography,
Proceedings of the XV International Conference on Hyperbolic Problems: Theory, Numerics and Applications,
Bulletin of the Brazilian Mathematical Society, Springer, 47 (2016), pp. 91-103.

A. Chertock, S. Cui, A. Kurganov, and T. Wu,
Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms,
International Journal for Numerical Methods in Fluids, 78 (2015), pp. 355-383.

A. Chertock, S. Cui, A. Kurganov and T. Wu,
Steady state and sign preserving semi-implicit Runge-Kutta methods for ODEs with stiff damping term,
SIAM Journal on Numerical Analysis, 53 (2015), pp. 2008-2029.

A. Chertock, J.-G. Liu and T. Pendleton,
Elastic collisions among peakon solutions for the Camassa-Holm equation,
Applied Numerical Mathematics, 93 (2015), pp. 30-46.

J. A. Carrillo, A. Chertock, and Y. Huang,
A finite-volume method for nonlinear nonlocal equations with a gradient flow structure,
Communications in Computational Physics, 17 (2015), pp. 233-258.

M. Castro Diaz, Y. Cheng, A. Chertock, and A. Kurganov,
Solving two-mode shallow water equations using finite volume methods,
Communications in Computational Physics, 16 (2014), pp. 1323-1354.

A. Chertock, M. Herty and A. Kurganov,
An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs,
Computational Optimization and Applications, 59, (2014), pp. 689-724.

A. Chertock, A. Kurganov and Y. Liu,
Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients,
Numerische Mathematik, 127 (2014), pp. 595-639.

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 Modeling 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.