Publications
Joshua Lee Padgett's articles on arXiv.
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 highdimensional semilinear partial differential equations, 2021 (submitted).

arXiv:2109.05345

J. L. Padgett and E. Servin^{*}, A positivity and monotonicitypreserving nonlinear operator splitting approach for approximating solutions to quenchingcombustion 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 datadriven 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 semicrystalline 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 onedimensional 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. 715739, 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. 163179, 2019. Official link

arXiv:1901.06049

M. A. Beauregard and J. L. Padgett, A variable nonlinear splitting algorithm for reactiondiffusion systems with self and crossdiffusion, Numerical Methods for Partial Differential Equations, Volume 35, Issue 2, pp. 597614, 2019. Official link

arXiv:1901.06605

J. L. Padgett, The quenching of solutions to timespace fractional Kawarada problems, Computers and Mathematics with Applications, Volume 76, Issue 7, pp. 15831592, 2018. Official link

arXiv:1901.10039

J. L. Padgett and Q. Sheng, Numerical solution of degenerate stochastic Kawarada equations via a semidiscretized approach, Applied Mathematics and Computation, Volume 325, pp. 210226, 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 CrankNicolson scheme for solving the stochastic Kawarada equation via arbitrary grids, Numerical Methods for Partial Differential Equations, Volume 33, pp. 13051328, 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 selfdiffusion, Journal of Computational and Applied Mathematics, Volume 321, pp. 825, 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 quenchingcombustion equations, Modern Mathematical Methods and High Performance Computing in Science and Technology, EditorinChief: V. K. Singh, Springer Verlag, Singapore, pp. 155167, 2016. Official link

arXiv:1901.06356

J. L. Padgett and Q. Sheng, On the positivity, monotonicity, and stability of a semiadaptive LOD method for solving threedimensional degenerate Kawarada equations, Journal of Mathematical Analysis and Applications, Volume 439, Issue 2, pp. 465480, 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 highdimensional 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 spacetime solutions of highdimensional 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 LieTrotter stochastic operator splitting, (in preparation).