# Publications

### Publications

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*,

preprint.

A. Chertock, S. Jin and A. Kurganov,

*An operator splitting based stochastic Galerkin method for the one-dimensional compressible Euler equations with uncertainty*,

preprint.

A. Chertock, T. Izgin and P. Öffner,

*A stability analysis of a semi-implicit Runge–Kutta scheme for a nonlinear system*,

preprint.

A. Chertock, S. Cui, A. Kurganov, and C, Wang,

*A hybrid finite-difference-particle method for chemotaxis models*,

submitted.

A. Chertock, A. S. Iskhakov, S. Janajra, and A. Kurganov,

*Spline-based stochastic collocation methods for uncertainty quantification in nonlinear hyperbolic PDEs*,

submitted.

A. Chertock, A. Kurganov, M. Redle and V. Zeitlin,

*Divergence-free flux globalization based well-balanced path-conservative central-upwind schemes for
rotating shallow water magnetohydrodynamics*, submitted.

A. Chertock, S. Chu and A. Kurganov,

*An accurate deterministic projection method for two-dimensional stiff detonation waves*,

Communications in Mathematics Sciences, 22 (2024), pp. 871-910.

A. Chertock, C. Leonard, and S. Tsynkov,

*Finding the shape of lacunae of the wave equation using artificial neural networks*,

Applied Mathematics and Computation, (2023), accepted.

A. Chertock, M. Herty, A. S. Iskhakov, S. Janajra, A. Kurganov, and M. Lukacova-Medvidova,

*New high-order numerical methods for hyperbolic systems of nonlinear PDEs with uncertainties*,

Communications on Applied Mathematics and Computation, (2024)

https://doi.org/10.1007/s42967-024-00392-z

A. Chertock, A. Kurganov, M. Redle and K. Wu,

*A new locally divergence-free path-conservative central-upwind scheme for ideal
and shallow water magnetohydrodynamics*,

SIAM Journal on Scientific Computing, 46 (2024), pp. A1998-A2024.

A. Chertock and C. Leonard,

*Simulating partial differential equations with neural network*,

Proceedings of the XVIII International Conference on Hyperbolic Problems:

Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series,

vol 35. Springer, Cham., (2024).

A. Chertock, C. Leonard, S. Tsynkov, and S. Utyuzhnikov,

*Denoising convolution algorithms and applications to SAR signal processing*,

Communications on Analysis and Computation, 1 (2023), pp. 135-156.

A. Chertock, S. Chu, and A. Kurganov,

*Adaptive high-order A-WENO schemes based on a new local smoothness indicator*,

East Asian Journal on Applied Mathematics, 13 (2023), pp. 576-609.

C. Wang, A. Chertock, S. Cui, A. Kurganov, and Z. Zhang,

*A diffuse-domain based numerical method for a chemotaxis-fluid model*,

Mathematical Models and Methods in Applied Sciences, 33 (2023), pp. 341–375.

A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, B. Wiebe,

*Stochastic Galerkin method for cloud simulation. Part II: A fully random Navier-Stokes-cloud model*,

Journal of Computational Physics, 479 (2023), Paper No. 111987, 24 pp.

A. Chertock, S. Chu, M. Herty, A. Kurganov, M. Lukacova-Medvidova,

*Local characteristic decomposition based central-upwind scheme*,

Journal of Computational Physics, 473 (2023), Paper No. 111718, 24 pp.

A. Chertock, A. Kurganov, T. Wu and J. Yan,

*Well-balanced numerical method for atmospheric flow equations with gravity*,

Applied Mathematics and Computation, 439 (2023), Paper No. 127587, 13 pp.

A. Chertock, P. Degond, G. Dimarco, M. Lukacova-Medvidova, A. Ruhi,

*On a hybrid continuum-kinetic model for complex fluids*,

Partial Differential Equations and Applications, 3 (2022), no. 5, Paper No. 63, 28 pp.

A. Chertock, A. Kurganov, X. Liu, Y. Liu, and T. Wu,

*Well-balancing via flux globalization: Applications to shallow water equations with wet/dry fronts*,

Journal of Scientific Computing, 90 (2022), no. 1, Paper No. 9, 21 pp.

A. Chertock, S. Chu, and A. Kurganov,

*Hybrid multifluid algorithms based on the path-conservative central-upwind scheme*,

Journal of Scientific Computing, 89 (2021), no. 2, Paper No. 48, 24 pp.

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

*Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography*,

Communications in Mathematical Sciences, 18 (2020), pp. 2149–2168.

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

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

Proceedings of the XVII International Conference on Hyperbolic Problems:

Theory, Numerics and Applications, American Institute of Mathematical Sciences, 10 (2020), pp. 25-42.

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

*Finite-volume-particle methods for the two-component Camassa-Holm system*,

Communications in Computational Physics, 27 (2020), pp. 480-502.

X. Liu, A. Chertock, A. Kurganov, and K. Wolfkill,*
One-dimensional/two-dimensional coupling approach with quadrilateral confluence region for modeling river systems*,

Journal of Scientific Computing, 81 (2019), pp. 1297-1328.

A. Chertock, A. Ditkowski, A. Gelb, S. Gottlieb, S. Tsynkov,

Preface to the special issue in memory of Professor Saul Abarbanel [Editorial],

Journal of Scientific Computing, 81 (2019), pp. 1119–1123.

A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, and B. Wiebe,

*Stochastic Galerkin method for cloud simulation*,

Mathematics of Climate and Weather Forecasting, 5 (2019), pp. 65-106.

A. Chertock and A. Kurganov,

*High-resolution positivity and asymptotic preserving numerical methods for chemotaxis and related models*,

Active Particles, Volume 2. Modeling and Simulation in Science, Engineering and Technology,

Springer International Publishing, Birkhauser (2019), pp. 109-148.

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,

Mathematical Biosciences and Engineering, 16 (2019), pp. 5804–5835.

A. Chertock, A. Kurganov, M. Ricchiuto and T. Wu,

*Adaptive moving mesh upwind scheme for the two-species chemotaxis model*,

Computers and Mathematics with Applications, 77 (2019), pp. 3172-3185.

Y. Cheng, A. Chertock, M. Herty, A. Kurganov, and T. Wu,

A new approach for designing moving-water equilibria preserving schemes for the shallow water equations,

Journal of Scientific Computing, 80 (2019), pp. 538–554.

X. Liu, A. Chertock, and A. Kurganov,

*An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces*,

Journal of Computational Physics, 391 (2019), pp.259-279.

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, 12 (2019), pp.195-216.

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:

Theory, Numerics and Applications of Hyperbolic Problems I, Springer, 236 (2018), pp. 345-361.

A. Chertock, S. Cui, A. Kurganov, S. Ozcan and E Tadmor,

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes,

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,

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 and 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 and 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 and A. Kurganov,

On a hybrid final-volume-particle method,

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

A. Chertock and 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 and D. Levy,

A particle method 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 and 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 and 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.

Yu. N. Karamzin, V. A. Trofimov and Chertok, A. E.,

An algorithm for the numerical solution of equations describing processes in photoreceivers.

Journal of Mathematical Modeling, 3 (1991), pp. 95-103 (in Russian).