I am currently a Postdoctoral Research Associate in the Department of Mathematics and Statistics at Texas Tech University. I received my Ph.D. in Mathematics from Baylor University in August 2017 under the advisement of Qin "Tim" Sheng. Before that I received my B.S. in Mathematics from Gardner-Webb University, where I also was a member of the Track and Field team (I competed in the javelin and hammer throw). My undergraduate studies also included cellular biology, which led to several semesters worth of research into various aspects of cancer metabolism.
J. L. Padgett and Q. Sheng,
Convergence of an operator splitting scheme for abstract stochastic evolution equations, Advances in Mechanics and Mathematics
(to appear).
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, Vol. 35, Issue 2, 2019, pp. 597-614. doi:10.1002/num.22315
J. L. Padgett,
The quenching of solutions to time-space fractional Kawarada problems, Computers and Mathematics with Applications, Vol. 76, Issue 7, 2018, pp. 1583-1592. doi:10.1016/j.camwa.2018.07.009
J. L. Padgett and Q. Sheng, Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach, Applied Mathematics and Computation,
Vol. 325, 2018, pp. 210-226. doi:10.1016/j.amc.2017.12.034
E. G. Kostadinova, K. Busse, N. Ellis, J. L. Padgett, C. D. Liaw, L. S. Matthews, T. W. Hyde, Delocalization in infinite disordered 2D lattices of different geometry,
Physical Review B, Vol. 96, 235408, 2017. doi:10.1103/PhysRevB.96.235408
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, Vol. 33, 2017, pp. 1305-1328. doi:10.1002/num.22144
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,
Vol. 321, 2017, pp. 8-25. doi:10.1016/j.cam.2017.02.019
(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, 2016, pp. 155-167. doi:10.1007/978-981-10-1454-3_13
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 Vol. 439, 2016, pp. 465-480. doi:10.1016/j.jmaa.2016.02.071
Solving Degenerate Stochastic Kawarada Partial Differential Equations via Adaptive Splitting Methods. Official link
Drafts
Below are a list of manuscripts currently in preparation (and exist in various stages of the preparation process):
(not on arXiv, yet)
J. L. Padgett, E. G. Kostadinova, C. D. Liaw, K. Busse, L. S. Matthews, and T. W. Hyde, Anomalous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method, (in preparation).
(not on arXiv, yet)
J. L. Padgett, Weak convergence of the abstract Lie-Trotter stochastic operator splitting, (in preparation).
(not on arXiv, yet)
J. L. Padgett, Operator splitting techniques for the Mittag-Leffler operator, (in preparation).
(not on arXiv, yet)
J. L. Padgett and J. Miller, The Hopf algebraic structure of numerical integrators for time-fractional differential equations, (in preparation).
Many of my presentations are contributions to the wonderful seminars maintained by the department, here at Texas Tech University. Those interested may find more information about these seminars in the links below: