Joshua Lee Padgett

Postdoctoral Research Associate

Department of Mathematics and Statistics
Texas Tech University
Broadway and Boston
Lubbock, Texas 79409-1042

Email:
joshua.padgett@ttu.edu

Office: MATH 219

profile


Research Interests

Publications

Drafts

Presentations

People

Teaching

Resources

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.

Here is a copy of my most recent Curriculum Vitae

Joshua Lee Padgett's Google Scholar profile.

Joshua Lee Padgett's ResearchGate profile.

A link with the information regarding the JMM Special Session I am co-organizing, may be found here.

Research Interests

Topics of interest: Applied mathematics, numerical analysis, nonlinear analysis, geometric and Lie group integration methods, operator splitting methods, quenching-combustion differential equations, nonlinear differential equations, fractional differential equations, stochastic differential equation, scientific computing

Detailed research interests.

Publications

Joshua Lee Padgett's articles on arXiv.

Below are a list of accepted publications.

arXiv:1902.03503
J. L. Padgett, Analysis of an approximation to a fractional extension problem, (submitted).
arXiv:1901.06371
J. L. Padgett and Q. Sheng, Convergence of an operator splitting scheme for abstract stochastic evolution equations, Advances in Mechanics and Mathematics (to appear).
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, Vol. 35, Issue 2, 2019, pp. 597-614. doi:10.1002/num.22315
arXiv:1901.06605
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
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, Vol. 325, 2018, pp. 210-226. doi:10.1016/j.amc.2017.12.034
arXiv:1706.02800
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
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, Vol. 33, 2017, pp. 1305-1328. doi:10.1002/num.22144
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, 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
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 Vol. 439, 2016, pp. 465-480. doi:10.1016/j.jmaa.2016.02.071


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 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).

Presentations

Here is a link to a list of my invited and contributed talks.

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:

Applied Math Seminar

Analysis Seminar

Geometry Seminar

Teaching

Request an appointment with me.

More information regarding my courses may be found below or by logging into Blackboard (if you are a student).

Courses taught at Texas Tech University:

Fall 2019:
MATH 4330 (Mathematical Computing)
Fall 2019:
MATH 5099 (Numerical Methods for Singular and Nonlinear Differential Equations)
Fall 2019:
MATH 5368 (Abstract Algebra Applied I)
Summer 2019:
MATH 2360 (Linear Algebra)
Summer 2019:
MATH 4330 (Mathematical Computing)
Spring 2019:
MATH 5369 (Abstract Algebra Applied II)
Fall 2018:
MATH 5368 (Abstract Algebra Applied I)
Summer 2018:
MATH 4330 (Mathematical Computing)
Summer 2018:
MATH 3360 (Foundations of Algebra)
Spring 2018:
MATH 3430 (Computational Techniques for Science and Mathematics)
Fall 2017:
MATH 2450 (Calculus III), 2 sections

Courses taught at Baylor University:
Spring 2017:
MTH 3326 (Partial Differential Equations)
Spring 2017:
CSI 2350 (Discrete Structures)
Fall 2016:
MTH 2321 (Calculus III)
Spring 2016:
MTH 1322 (Calculus II)
Fall 2015:
MTH 1321 (Calculus I)
Spring 2015:
MTH 1321 (Calculus I)
Fall 2014:
MTH 1309 (Calculus for Business Students)
Spring 2014:
MTH 1320 (Precalculus)
Fall 2013:
MTH 1320 (Precalculus)


You can find some useful material for getting started with LaTeX here (intended for students with zero LaTeX knowledge).

Resources

MathSciNet • arXiv • MathOverflow • Kerodon • Library Genesis • Sci-Hub 1 • Sci-Hub 2 • Sci-Hub 3 • Google Scholar