Students

  • Philip Zaleski, Ph.D. Student
    Department of Mathematical Sciences, NJIT
  • Austin Juhl, Ph.D. Student
    Department of Mathematical Sciences, NJIT
  • William (Joe) McCann, BS 2020, MS 2021, Summer 2021
    Department of Mathematical Sciences, NJIT
    Thesis: Stationary probability distributions of stochastic gradient descent and the success and failure of the diffusion approximation
  • Linwan Feng, Ph.D., Summer 2020
    Co-advised with Wooyoung Choi
    Department of Mathematical Sciences, NJIT
    Thesis: Efficient time-stepping approaches for the dispersive shallow water equations
  • Mahdi Bandegi, Ph.D., Fall 2019
    Department of Mathematical Sciences, NJIT
    Thesis: Convex relaxations of a continuum aggregation model, and their efficient numerical solution


  • Preprints

  • A. Biswas, D. Ketcheson, S. Roberts, B. Seibold, D. Shirokoff
    Explicit Runge Kutta Methods that Alleviate Order Reduction


  • Publications

  • A. Biswas, D. Ketcheson, B. Seibold, D. Shirokoff
    Algebraic structure of the weak stage order conditions for Runge-Kutta methods
    SIAM Journal on Numerical Analysis, 62,1 (2024), pp. 48-72.
  • R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
    Spatial manifestations of order reduction in Runge-Kutta methods for initial boundary value problems
    Communications in Mathematical Sciences, 22, 3, (2024), pp 613-653.
  • A. Biswas, D. Ketcheson, B. Seibold, D. Shirokoff
    Design of DIRK schemes with high weak stage order
    Communications in Applied Mathematics and Computational Science 18, 1 (2023), pp 1-28.
  • R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
    High-order finite element methods for a pressure Poisson equation reformulation of the Navier-Stokes equations with electric boundary conditions
    Computer Methods in Applied Mechanics and Engineering, 373, 1 January (2021), 113451.
  • D. Ketcheson, B. Seibold, D. Shirokoff, D. Zhou
    DIRK Schemes with high weak stage order
    In: Sherwin S., Moxey D., Peiro J., Vincent P., Schwab C. (eds)
    Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018.
    Lecture Notes in Computational Science and Engineering, vol 134. Springer, Cham.
  • W. Batson, L. Cummings, D. Shirokoff, L. Kondic
    Oscillatory thermocapillary instability of a film heated by a thick substrate
    Journal of Fluid Mechanics, 872 (2019), pp 928-962.
  • B. Seibold, D. Shirokoff, D. Zhou
    Unconditional stability for multistep ImEx schemes: Practice
    Journal of Computational Physics, 376, 1, (2019), pp 295-321.
  • M. Bandegi, D. Shirokoff
    Approximate global minimizers to pairwise interaction problems via convex relaxation
    SIAM Journal on Applied and Dynamical Systems, 17, 1, (2018), pp 417-456.
  • R. R. Rosales, B. Seibold, D. Shirokoff, D. Zhou
    Unconditional stability for multistep ImEx schemes: Theory
    SIAM Journal on Numerical Analysis, 55, 5, (2017), pp 2336-2360.
  • R. Galagusz, D. Shirokoff, J-C. Nave
    A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries
    Journal of Computational Physics, 306, 1, (2016), pp 167-198,
  • X. Cheng, D. Li, D. Shirokoff, B. Wetton
    On the spectral gap of a square distance matrix
    Journal of Statistical Physics, 166, 3-4, (2016), pp 1029-1035.
  • D. Shirokoff, J-C. Nave
    A Sharp-interface active penalty method for the incompressible Navier-Stokes equations
    Journal of Scientific Computing, 62, 1, (2015), pp 53-77.
  • D. Shirokoff, R. Choksi, J-C. Nave
    Sufficient conditions for global minimality of metastable states in a class of non-convex functionals: a simple approach via quadratic lower bounds
    Journal of Nonlinear Science, 25, 3, (2015), pp 539-582.
  • D. Zhou, B. Seibold, D. Shirokoff, P. Chidyagwai, R. Rosales
    Meshfree finite differences for a vector Poisson and pressure Poisson equation with electric boundary conditions
    Meshfree methods for Partial Differential Equations VII
    Lecture Notes in Computational Science and Engineering,
    Vol. 100 Griebel, M. and Schweitzer, M.A. (ed.), Springer (2014).
  • D. Shirokoff
    Bouncing droplets on a billiard table
    Chaos: An Interdisciplinary Journal of Nonlinear Science, 23, 013115 (2013).
  • D. Shirokoff, R. R. Rosales
    An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
    Journal of Computational Physics, 230, 23, (2011), pp 8619-8646.
  • D. Shirokoff
    Renormalized waves and thermalization of the Klein-Gordon equation
    Physical Review E, 83, 046217, (2011).
  • M. A. Amin, D. Shirokoff
    Flat-top oscillons in an expanding universe
    Physical Review D, 81, 085045 (2010).
  • D. Shirokoff, C. H. F. Fung, H. K. Lo
    Discrete rotational symmetry and quantum key distribution protocols
    Physical Review A, 75, 032341 (2007).
  • K. Samokhin, D. Shirokoff
    Phenomenological theory of superconductivity near domain walls in ferromagnets
    Physical Review B, 71, 104527 (2005).


  • Theses

  • I. A pressure Poisson method for the incompressible Navier-Stokes equations : II. Long time behavior of the Klein-Gordon equations, Ph.D. Thesis, Massachusetts Institute of Technology, 2011.
  • Discrete rotational symmetry and quantum key distribution protocols, Undergraduate Thesis, University of Toronto, 2006.


  • Grants

  • NSF DMS-2309727
    August 1, 2023 - July 31, 2026
  • NSF DMS-2012268
    August 15, 2020 - July 31, 2023
  • NSF DMS-1719693
    August 1, 2017 - July 31, 2020
  • Simons Foundation #359610
    Collaboration Grant for Mathematicians
    September 1, 2015 - August 31, 2017