Publications


  • 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, J.-G. Liu and T. Pendleton,
    Elastic collisions among peakon solutions for the Camassa-Holm equation,
    submitted.

  • A. Chertock, A. Kurganov, Z. Qu and T. Wu,
    On a three-layer approximation of two-layer shallow water equations,
    submitted.

  • A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev,
    Pedestrian flow models with slowdown interactions,
    accepted.

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

  • A. Chertock, A. Kurganov and Y. Liu,
    Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients,
    submitted.

  • A. Chertock, M. Herty and A. Kurganov,
    An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs,
    submitted.

  • 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.