#### Filter Results:

- Full text PDF available (18)

#### Publication Year

1999

2017

- This year (1)
- Last 5 years (10)
- Last 10 years (24)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Cell Type

#### Key Phrases

#### Method

#### Organism

Learn More

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind… (More)

- Elazar Zelzer, William McLean, +5 authors Bjorn Reino Olsen
- Development
- 2002

Angiogenesis is an essential component of skeletal development and VEGF signaling plays an important if not pivotal role in this process. Previous attempts to examine the roles of VEGF in vivo have been largely unsuccessful because deletion of even one VEGF allele leads to embryonic lethality before skeletal development is initiated. The availability of… (More)

- William McLean, Jane Gillis, Ron Waller
- Canadian respiratory journal
- 2003

OBJECTIVES
Despite advances in recent years, asthma morbidity and mortality have been noted to be on the increase in the past decade. The present study examined the failures and recommendations of past studies and introduced a new milieu for asthma care--the community pharmacy. The study incorporated a care protocol with the important ingredients of asthma… (More)

- Kassem Mustapha, William McLean
- SIAM J. Numerical Analysis
- 2013

We consider an initial-boundary value problem for ∂tu−∂ t ∇2u = f(t), that is, for a fractional diffusion (−1 < α < 0) or wave (0 < α < 1) equation. A numerical solution is found by applying a piecewise-linear, discontinuous Galerkin (DG) method in time combined with a piecewiselinear, conforming finite element method in space. The time mesh is graded… (More)

- William McLean, Kassem Mustapha
- Numerische Mathematik
- 2007

In a previous paper, McLean and Thomée (to appear), we studied three numerical methods for the discretization in time of a fractional order evolution equation, in a Banach space framework. Each of the methods applied a quadrature rule to a contour integral representation of the solution in the complex plane, where for each quadrature point an elliptic… (More)

- William McLean, Kassem Mustapha
- Numerical Algorithms
- 2008

We employ a piecewise-constant, discontinuous Galerkin method for the time discretization of a sub-diffusion equation. Denoting the maximum time step by k, we prove an a priori error bound of order k under realistic assumptions on the regularity of the solution. We also show that a spatial discretization using continuous, piecewise-linear finite elements… (More)

- William McLean, Ian H. Sloan, Vidar Thomée
- Numerische Mathematik
- 2006

- Michael D. Risley, David R. Garrod, Mark J Henkemeyer, William McLean
- Mechanisms of Development
- 2009

Ephs and ephrins are cell surface receptors that bind to each other and initiate distinct, bidirectional signalling pathways in processes known as forward (Eph) and reverse (ephrin) signalling. Previous work had shown that the loss of ephrinB1 protein alone or compound loss of EphB2 and EphB3 leads to cleft palate. Because of the bidirectional signalling… (More)

- William McLean
- 2007

We consider the discretization in time of a fractional order diffusion equation. The approximation is based on a further development of the approach of using Laplace transformation to represent the solution as a contour integral, evaluated to high accuracy by quadrature. This technique reduces the problem to a finite set of elliptic equations with complex… (More)