21 citations · 47 across the 7 of their papers we have counts for
7 papers
A series representation of the discrete fractional Laplace operator of arbitrary order
Tiffany Frugé Jones, Evdokiya Georgieva Kostadinova, Joshua Lee Padgett +1
Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are gre…
Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces
Tiffany Frugé Jones, Joshua Lee Padgett, Qin Sheng
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution…
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…
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…
On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations
Joshua L. Padgett, Qin Sheng
This paper concerns the numerical solution of three-dimensional degenerate Kawarada equations. These partial differential equations possess highly nonlinear source terms, and exhib…
An Effective -Stretching Adaptive Finite Difference Method for Paraxial Light Beam Propagation Simulations
Leonel Gonzalez, Shekhar Guha, James W. Rogers +1
A new -stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing p…