23 citations · 127 across the 19 of their papers we have counts for
8 papers · 1 filter
Anomalous Diffusion in One-Dimensional Disordered Systems: A Discrete Fractional Laplacian Method
J. L. Padgett, E. G. Kostadinova, C. D. Liaw +3
This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one…
Analysis of an approximation to a fractional extension problem
Joshua L Padgett
The purpose of this work is to study an approximation to an abstract Bessel-type problem, which is a generalization of the extension problem associated with fractional powers of th…
Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach
Joshua L Padgett, Qin Sheng
The numerical solution of a highly nonlinear two-dimensional degenerate stochastic Kawarada equation is investigated. A semi-discretized approximation in space is comprised on arbi…
The quenching of solutions to time-space fractional Kawarada problems
Joshua L Padgett
Quenching solutions to a Kawarada problem with a Caputo time-fractional derivative and a fractional Laplacian are considered. The solutions to such problems may only exist locally…
Convergence of an operator splitting scheme for abstract stochastic evolution equations
Joshua L Padgett, Qin Sheng
In this paper we study the convergence of a Lie-Trotter operator splitting for stochastic semi-linear evolution equations in a Hilbert space. The abstract Hilbert space setting all…
On a Nonuniform Crank-Nicolson Scheme for Solving the Stochastic Kawarada Equation via Arbitrary Grids
Joshua L Padgett, Qin Sheng
This paper studies a nonuniform finite difference method for solving the degenerate Kawarada quenching-combustion equation with a vibrant stochastic source. Arbitrary grids are int…