Publications

Below are a list of accepted (or submitted) publications. Note that authors are listed in alphabetical order and graduate students are designated with an ^*.

arXiv:2110.08297: M. Hutzenthaler, A. Jentzen, B. Kuckuck, and J. L. Padgett, Strong L^p-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations, 2021 (submitted).
arXiv:2109.05345: J. L. Padgett and E. Servin^*, A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations , 2021 (submitted).
arXiv:2102.09344: R. Banka^*, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer, Physics of Plasmas, Volume 28, Issue 7, 2021. Official link
arXiv:2101.03629: T. F. Jones, E. G. Kostadinova, J. L. Padgett, and Q. Sheng, A series representation of the discrete fractional Laplace operator of arbitrary order, Journal of Mathematical Analysis and Applications, Volume 504, Issue 1, 2021. Official link
arXiv:2012.11092: T. F. Jones, J. L. Padgett, and Q. Sheng, Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces, From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory, pp. 265–279, 2021. Official link
arXiv:2008.02740: S. Gautam^*, Y. Geldiyev^*, A. Ibraguimov, Y. Mechref, J. L. Padgett, and W. Peng, Object classification in analytical chemistry via data-driven discovery of partial differential equations, Computational and Mathematical Methods, Volume 3, Issue 4, 2021. Official link
arXiv:2006.01068: T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in semi-crystalline polymer structures, Physical Review Research, Volume 2, Issue 4, 2020. Official link
arXiv:1907.10824: K. Busse^*, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method, Journal of Physics A: Mathematical and Theoretical, Volume 53, Issue 13, 135205, 2020. Official link
arXiv:1902.03503: J. L. Padgett, Analysis of an approximation to a fractional extension problem, BIT Numerical Mathematics, Volume 60, pp. 715-739, 2019. Official link
arXiv:1901.06371: J. L. Padgett and Q. Sheng, Convergence of an operator splitting scheme for abstract stochastic evolution equations, Advances in Mathematical Methods and High Performance Computing, Springer, pp. 163-179, 2019. Official link
arXiv:1901.06049: M. A. Beauregard and J. L. Padgett, A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion, Numerical Methods for Partial Differential Equations, Volume 35, Issue 2, pp. 597-614, 2019. Official link
arXiv:1901.06605: J. L. Padgett, The quenching of solutions to time-space fractional Kawarada problems, Computers and Mathematics with Applications, Volume 76, Issue 7, pp. 1583-1592, 2018. Official link
arXiv:1901.10039: J. L. Padgett and Q. Sheng, Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach, Applied Mathematics and Computation, Volume 325, pp. 210-226, 2018. Official link
arXiv:1706.02800: K. Busse, N. Ellis, T. W. Hyde, E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and J. L. Padgett, Delocalization in infinite disordered 2D lattices of different geometry, Physical Review B, Volume 96, Issue 23, 235408, 2017. Official link
arXiv:1901.06365: J. L. Padgett and Q. Sheng, Nonuniform Crank-Nicolson scheme for solving the stochastic Kawarada equation via arbitrary grids, Numerical Methods for Partial Differential Equations, Volume 33, pp. 1305-1328, 2017. Official link
arXiv:1510.07694: M. A. Beauregard, J. L. Padgett, and R. D. Parshad, A nonlinear splitting algorithm for systems of partial differential equations with self-diffusion, Journal of Computational and Applied Mathematics, Volume 321, pp. 8-25, 2017. Official link
(not on arXiv): J. L. Padgett and Q. Sheng, On the stability of a variable step exponential splitting method for solving multidimensional quenching-combustion equations, Modern Mathematical Methods and High Performance Computing in Science and Technology, Editor-in-Chief: V. K. Singh, Springer Verlag, Singapore, pp. 155-167, 2016. Official link
arXiv:1901.06356: J. L. Padgett and Q. Sheng, On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations, Journal of Mathematical Analysis and Applications, Volume 439, Issue 2, pp. 465-480, 2016. Official link

Below is a link to my dissertation:

Personal PDF file: Solving Degenerate Stochastic Kawarada Partial Differential Equations via Adaptive Splitting Methods. Official link

Drafts

Below are a list of manuscripts and projects currently in preparation (or actively being pursued):

(not on arXiv, yet): A. Jentzen, B. Kuckuck, and J. L. Padgett, Overcoming the curse of dimensionality in the approximation of high-dimensional nonlinear partial differential equations via deep neural networks in the L^p-sense, (in final stages).
(not on arXiv, yet): A. Jentzen, B. Kuckuck, and J. L. Padgett, Expressivity of deep neural networks for space-time solutions of high-dimensional nonlinear PDEs, (in preparation).
(not on arXiv, yet): J. Miller, J. L. Padgett, R. Ramirez^*, On the construction of stochastic operator splitting methods of arbitrarily high order via Hopf algebraic techniques, (in preparation).
(not on arXiv, yet): J. L. Padgett, Weak convergence of the abstract Lie-Trotter stochastic operator splitting, (in preparation).