Zobrazeno 1 - 10
of 421
pro vyhledávání: '"McLean, William"'
In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on the parametr
Externí odkaz:
http://arxiv.org/abs/2409.00893
Publikováno v:
Journal of Scientific Computing, 2024
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear interpola
Externí odkaz:
http://arxiv.org/abs/2401.04946
Autor:
McLean, William
Publikováno v:
Calcolo 58:7, 2021
The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point of differ
Externí odkaz:
http://arxiv.org/abs/2208.03851
Autor:
McLean, William, Mustapha, Kassem
We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most $r-1$ in $t$, for $r\ge1$ and with maximum step size~$k$. It is well known that the spatial $L_2
Externí odkaz:
http://arxiv.org/abs/2208.03846
Autor:
McLean, William Wade, 1951
The purpose of this study was to investigate the perceptions of beginning and experienced teachers as they relate to the leadership behaviors a principal should exhibit that would assist teachers in becoming more effective classroom teachers. To acco
Externí odkaz:
http://hdl.handle.net/10150/298762
Autor:
McLean, William, Mustapha, Kassem
Publikováno v:
Numerical Algorithms 89:1441-1463 (2022)
We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded uniformly in
Externí odkaz:
http://arxiv.org/abs/2012.13860
Implementation of high-order, discontinuous Galerkin time stepping for fractional diffusion problems
Autor:
McLean, William
Publikováno v:
ANZIAM J. 62: 121-147, 2020
The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily evaluated. We desc
Externí odkaz:
http://arxiv.org/abs/2003.09805
Publikováno v:
SIAM Journal on Scientific Computing, Vol. 40, Issue 6, 2018, http://epubs.siam.org/toc/sjoce3/40/6
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on time as well
Externí odkaz:
http://arxiv.org/abs/1902.03204
Publikováno v:
Commun. Pure Appl. Anal. 18(5), 2765-2787, 2019
A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator $u_t-\nabla\cdot(\partial_t^{1-\alpha}\kappa_\alpha\nabla u-\textbf{F}\partial_t^{1-\alpha}u)$, where $0<\alpha <1$. The forcing function $\textb
Externí odkaz:
http://arxiv.org/abs/1902.02564