Works (67)

2020 journal article

Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 27(2), 480–502.

By: A. Chertock, A. Kurganov & Y. Liu

Sources: Web Of Science, ORCID
Added: December 30, 2019

2019 journal article

A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations

JOURNAL OF SCIENTIFIC COMPUTING, 80(1), 538–554.

By: Y. Cheng, A. Chertock, M. Herty, A. Kurganov & T. Wu

Sources: Web Of Science, ORCID
Added: June 17, 2019

2019 journal article

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

Computers & Mathematics with Applications, 77(12), 3172–3185.

By: A. Chertock, A. Kurganov, M. Ricchiuto & T. Wu

Sources: Web Of Science, Crossref, ORCID
Added: July 1, 2019

2019 journal article

An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions

Kinetic & Related Models, 12(1), 195–216.

By: A. Chertock, A. Kurganov, M. Lukáčová-Medvid’ová & Ș. Nur Özcan

Sources: ORCID, Crossref
Added: September 8, 2019

2019 journal article

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

JOURNAL OF COMPUTATIONAL PHYSICS, 391, 259–279.

By: X. Liu, A. Chertock & A. Kurganov

Sources: Web Of Science, ORCID
Added: June 17, 2019

2019 article

High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

ACTIVE PARTICLES, VOL 2: ADVANCES IN THEORY, MODELS, AND APPLICATIONS, pp. 109–148.

By: A. Chertock & A. Kurganov

Sources: Web Of Science, ORCID
Added: March 30, 2020

2019 journal article

Incompressible limit of a continuum model of tissue growth with segregation for two cell populations

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 16(5), 5804–5835.

By: A. Chertock, P. Degond, S. Hecht & J. Vincent

Sources: Web Of Science, ORCID
Added: July 8, 2019

2019 journal article

Incompressible limit of a continuum model of tissue growth with segregation for two cell populations

Math. Biosci. Eng., 16(5), 5804–5835.

By: A. Chertock, P. Degond, S. Hecht & J. Vincent

Source: ORCID
Added: September 8, 2019

2019 journal article

One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems

Journal of Scientific Computing.

Source: ORCID
Added: September 10, 2019

2019 journal article

Preface to the Special Issue in Memory of Professor Saul Abarbanel

Journal of Scientific Computing.

Source: ORCID
Added: September 15, 2020

2019 journal article

Stochastic Galerkin method for cloud simulation

Mathematics of Climate and Weather Forecasting, 5(1), 65–106.

By: A. Chertock, A. Kurganov, M. Lukáčová-Medvid’ová, P. Spichtinger & B. Wiebe

Sources: Crossref, ORCID
Added: December 11, 2019

2018 journal article

A second-order finite-difference method for compressible fluids in domains with moving boundaries

Commun. Comput. Phys., 23(1), 230–263.

By: A. Chertock, A. Coco, A. Kurganov & G. Russo

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2018 journal article

An asymptotic preserving scheme for kinetic models with singular limit

Kinet. Relat. Models, 11(4), 735–756.

By: A. Chertock, C. Tan & B. Yan

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2018 journal article

High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems

Adv. Comput. Math., 44(1), 327–350.

By: A. Chertock, Y. Epshteyn, H. Hu & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2018 chapter

Well-Balanced Central-Upwind Schemes for 2x2 Systems of Balance Laws

In Theory, Numerics and Applications of Hyperbolic Problems I (Vol. 236, pp. 345–361).

By: A. Chertock, M. Herty & Ş. Özcan

Sources: Crossref, ORCID
Added: August 30, 2019

2018 journal article

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

J. Comput. Phys., 358, 36–52.

By: A. Chertock, S. Cui, A. Kurganov, Ş. Özcan & E. Tadmor

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2018 journal article

Well-balanced schemes for the shallow water equations with Coriolis forces

Numer. Math., 138(4), 939–973.

By: A. Chertock, M. Dudzinski, A. Kurganov & M. Lukáčová-Medviďová

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2017 chapter

A Practical Guide to Deterministic Particle Methods

In Handbook of Numerical Analysis (Vol. 18, pp. 177–202).

By: A. Chertock

Sources: Crossref, ORCID
Added: August 6, 2018

2017 chapter

A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles

In Springer Proceedings in Mathematics & Statistics (Vol. 199, pp. 43–55).

By: Y. Cheng, A. Chertock & A. Kurganov

Sources: Crossref, ORCID
Added: August 6, 2018

2017 journal article

An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations

J. Comput. Phys., 335, 387–403.

By: A. Chertock, P. Degond & J. Neusser

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2017 journal article

Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

SMAI Journal of Computational Mathematics, 3, 139–180.

By: A. Chertock, S. Cui & A. Kurganov

Sources: Crossref, ORCID
Added: July 20, 2019

2016 journal article

Central-upwind scheme for shallow water equations with discontinuous bottom topography

Bull. Braz. Math. Soc. (N.S.), 47(1), 91–103.

By: A. Bernstein, A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2015 journal article

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

Commun. Comput. Phys., 17(1), 233–258.

By: J. Carrillo, A. Chertock & Y. Huang

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2015 journal article

Elastic collisions among peakon solutions for the Camassa-Holm equation

Appl. Numer. Math., 93, 30–46.

By: A. Chertock, J. Liu & T. Pendleton

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2015 journal article

Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term

SIAM Journal on Numerical Analysis, 53(4), 2008–2029.

By: A. Chertock, S. Cui, A. Kurganov & T. Wu

Sources: NC State University Libraries, ORCID, Crossref
Added: August 6, 2018

2015 journal article

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

Internat. J. Numer. Methods Fluids, 78(6), 355–383.

By: A. Chertock, S. Cui, A. Kurganov & T. Wu

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2014 journal article

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

Comput. Optim. Appl., 59(3), 689–724.

By: A. Chertock, M. Herty & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2014 journal article

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

Numer. Math., 127(4), 595–639.

By: A. Chertock, A. Kurganov & Y. Liu

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2014 journal article

Solving two-mode shallow water equations using finite volume methods

Commun. Comput. Phys., 16(5), 1323–1354.

By: M. Dı́az, Y. Cheng, A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2013 journal article

PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS

Mathematical Models and Methods in Applied Sciences, 24(02), 249–275.

By: A. Chertock, A. Kurganov, A. Polizzi & I. Timofeyev

Sources: NC State University Libraries, ORCID, Crossref
Added: August 6, 2018

2013 journal article

Three-layer approximation of two-layer shallow water equations

Math. Model. Anal., 18(5), 675–693.

By: A. Chertock, A. Kurganov, Z. Qu & T. Wu

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2012 journal article

CONVERGENCE OF A PARTICLE METHOD AND GLOBAL WEAK SOLUTIONS OF A FAMILY OF EVOLUTIONARY PDES

Siam Journal on Numerical Analysis, 50(1), 1–21.

By: A. Chertock, J. Liu & T. Pendleton

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2012 chapter

Convergence Analysis of the Particle Method for the Camassa-Holm Equation

In Series in Contemporary Applied Mathematics (Vol. 18, pp. 365–373).

By: A. Chertock, J. Liu & T. Pendleton

Sources: Crossref, ORCID
Added: July 20, 2019

2012 journal article

INTEGRATION OF THE EPDIFF EQUATION BY PARTICLE METHODS

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 46(3), 515–534.

By: A. Chertock, P. Toit & J. Marsden

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2012 journal article

ON A CHEMOTAXIS MODEL WITH SATURATED CHEMOTACTIC FLUX

Kinetic and Related Models, 5(1), 51–95.

By: A. Chertock, A. Kurganov, X. Wang & Y. Wu

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2012 journal article

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

Journal of Fluid Mechanics, 694, 155–190.

By: A. Chertock, K. Fellner, A. Kurganov, A. Lorz & P. Markowich

Sources: Crossref, ORCID
Added: July 20, 2019

2011 journal article

Central-Upwind Schemes for Boussinesq Paradigm Equations

Computational Science and High Performance Computing Iv, 115, 267–281.

By: A. Chertock, C. Christov, A. Kurganov, E. Krause, Y. Shokin, M. Resch, D. Kroner, N. Shokina

Source: ORCID
Added: August 27, 2019

2011 chapter

Central-upwind schemes for Boussinesq paradigm equations

In Computational science and high performance computing IV (Vol. 115, pp. 267–281).

By: A. Chertock, C. Christov & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2010 journal article

A Fast Explicit Operator Splitting Method for Passive Scalar Advection

Journal of Scientific Computing, 45(1-3), 200–214.

By: A. Chertock, C. Doering, E. Kashdan & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2010 chapter

On splitting-based numerical methods for convection-diffusion equations

In Numerical Methods for Balance Laws, Quaderni di Matematica, Aracne editrice S.r.l (Vol. 24, p. 303). Roma.

By: A. Chertock & A. Kurganov

Source: NC State University Libraries
Added: July 28, 2019

2009 journal article

Computing Multivalued Solutions of Pressureless Gas Dynamics by Deterministic Particle Methods

Communications in Computational Physics, 5(2-4), 565–581.

By: A. Chertock & A. Kurganov

Source: ORCID
Added: August 27, 2019

2009 conference paper

Computing multivalued solutions of pressureless gas dynamics by deterministic particle methods

Communications in Computational Physics, 5(2-4), 565–581.

By: A. Chertock & A. Kurganov

Source: NC State University Libraries
Added: August 6, 2018

2009 journal article

Fast explicit operator splitting method for convection-diffusion equations

International Journal For Numerical Methods in Fluids, 59(3), 309–332.

By: A. Chertock, A. Kurganov & G. Petrova

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2009 chapter

On splitting-based numerical methods for convection-diffusion equations

In Numerical methods for balance laws (Vol. 24, pp. 303–343). Dept. Math., Seconda Univ. Napoli, Caserta.

By: A. Chertock & A. Kurganov

Source: ORCID
Added: September 8, 2019

2008 journal article

A SIMPLE EULERIAN FINITE-VOLUME METHOD FOR COMPRESSIBLE FLUIDS IN DOMAINS WITH MOVING BOUNDARIES

Communications in Mathematical Sciences, 6(3), 531–556.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2008 journal article

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

Numerische Mathematik, 111(2), 169–205.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2008 journal article

INTERFACE TRACKING METHOD FOR COMPRESSIBLE MULTIFLUIDS

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 42(6), 991–1019.

By: A. Chertock, S. Karni & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2008 journal article

Modified Optimal Prediction and its Application to a Particle-Method Problem

Journal of Scientific Computing, 37(2), 189–201.

By: A. Chertock, D. Gottlieb & A. Solomonoff

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2008 chapter

Propagation of Diffusing Pollutant by a Hybrid Eulerian–Lagrangian Method

In Hyperbolic Problems: Theory, Numerics, Applications (pp. 371–379).

By: A. Chertock, E. Kashdan, A. Kurganov, S. BenzoniGavage & D. Serre

Sources: Crossref, ORCID
Added: July 20, 2019

2007 journal article

A new sticky particle method for pressureless gas dynamics

Siam Journal on Numerical Analysis, 45(6), 2408–2441.

By: A. Chertock, A. Kurganov & Y. Rykov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2006 journal article

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

Journal of Scientific Computing, 27(1-3), 189–199.

By: A. Chertock, A. Kurganov & G. Petrova

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2006 journal article

On a practical implementation of particle methods

Applied Numerical Mathematics, 56(10-11), 1418–1431.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2005 chapter

Conservative locally moving mesh method for multifluid flows

In Finite Volumes for Complex Applications IV (pp. 273–284). ISTE, London.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: July 28, 2019

2005 chapter

Fast explicit operator splitting method. Application to the polymer system

In Finite Volumes for Complex Applications IV: Vol. IV (pp. 63–72). ISTE, London.

By: A. Chertock, A. Kurganov & G. Petrova

Sources: NC State University Libraries, ORCID
Added: July 28, 2019

2005 journal article

On degenerate saturated-diffusion equations with convection

Nonlinearity, 18(2), 609–630.

By: A. Chertock, A. Kurganov & P. Rosenau

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2005 journal article

On wavelet-based numerical homogenization

Multiscale Modeling & Simulation, 3(1), 65–88.

By: A. Chertock & D. Levy

Sources: ORCID, NC State University Libraries
Added: August 6, 2018

2004 journal article

On a hybrid finite-volume-particle method

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 38(6), 1071–1091.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2003 journal article

Formation of discontinuities in flux-saturated degenerate parabolic equations

Nonlinearity, 16(6), 1875–1898.

By: A. Chertock, A. Kurganov & P. Rosenau

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2002 journal article

A Particle Method for the KdV Equation

Journal of Scientific Computing, 17(1-4), 491–499.

By: A. Chertock & D. Levy

Source: ORCID
Added: August 27, 2019

2002 journal article

On the stability of a class of self-similar solutions to the filtration-absorption equation

European Journal of Applied Mathematics, 13(2), 179–194.

By: A. Chertock

Sources: Crossref, ORCID
Added: July 20, 2019

2002 journal article

Particle methods for the KdV equation

Journal of Scientific Computing, 17, 491–499.

By: A. Chertock & D. Levy

Source: NC State University Libraries
Added: July 10, 2019

2001 journal article

Particle Methods for Dispersive Equations

Journal of Computational Physics, 171(2), 708–730.

By: A. Chertock & D. Levy

Sources: Crossref, ORCID
Added: July 20, 2019

2000 journal article

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

Proceedings of the National Academy of Sciences, 97(18), 9844–9848.

By: G. Barenblatt, M. Bertsch, A. Chertock & V. Prostokishin

Sources: Crossref, ORCID
Added: July 27, 2019

2000 journal article

Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, I

Journal of Computational Physics, 160(1), 42–66.

By: S. Abarbanel & A. Chertock

Sources: Crossref, ORCID
Added: July 20, 2019

2000 journal article

Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, II

Journal of Computational Physics, 160(1), 67–87.

By: S. Abarbanel, A. Chertock & A. Yefet

Sources: Crossref, ORCID
Added: July 20, 2019

1991 journal article

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

Mat. Model., 3(10), 95–103.

By: Y. Karamzin, V. Trofimov & A. Chertok

Source: ORCID
Added: September 8, 2019

1991 journal article

On a numerical algorithm for nonlinear differential equations describing some processes in photoreceivers

Journal of Mathematical Modeling, 3, 95–103.

By: A. Chertock, Y. Karamzin & V. Trofimov

Source: NC State University Libraries
Added: July 28, 2019

Employment

2002 - present

North Carolina State University Raleigh, NC, US
Professor and Head Mathematics

Education

1999 - 2001

University of California Berkeley Berkeley, CA, US
Postdoctoral Fellow Mathematics

1991 - 1999

Tel Aviv University Tel Aviv, IL
Ph.D. School of Mathematical Sciences

1984 - 1989

Lomonosov Moscow State University Moscow, RU
M.Sc. (Diploma of Higher Education) Faculty of Computational Mathematics and Cybernetics