Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Comparing the diffusion of online service recovery in small and large organisations

A key concern organisations face is how to incorporate Internet tools into their marketing communications mix. Where and how should companies invest their human, technological and financial resources? This paper explores a subset of this problem, online complaining and electronic customer service. It applies diffusion of innovation as a theoretical framework to investigate organisational implementation of email technology and explain the outcome of annual customer service surveys in 2001, 2002 and 2003. The results add to the small body of research on electronic service recovery by extending diffusion of innovations to email service recovery and underscoring the importance of adoption phases, particularly for SMEs. Larger companies provide more channels for submitting complaints, which represents an early phase of adoption. There was little difference in how large and small companies respond to online complaints, a later phase of adoption.

Developing within-company information and communication technologies (ICT) innovation diffusion networks : a study of three Australian major contractors

The innovation diffusion and knowledge management literature strongly supports the importance of communities of practice (COP) for enabling knowledge about how to use and adopt innovation initiatives. One of the most powerful tools for innovation diffusion is word-of-mouth wisdom from committed individuals who mentor and support each other. Close proximity for face-to-face interaction is highly effective, however, many organisations are geographically dispersed with projects being virtual linked sub-organisations using ICT to communicate. ICT has also introduced a useful facilitating technology for developing knowledge networks. This paper presents findings from a research program concentrating on ICT innovation diffusion in the Australian construction industry. One way in which ICT diffusion is taking place was found to be through within-company communities of practice. We undertook in-depth unstructured interviews with three of the major 10 to 15 contractors in Australia to discuss their ICT diffusion strategies. We discovered that in all three cases,within company networked communities of practice was a central strategy. Further, effective diffusion of ICT groupware tools can be critical in developing COP where they are geographically dispersed.

Supporting ICT diffusion in Australian construction organisations

Construction organisations comprise geographically dispersed virtually-linked suborganisations that work together to realise projects. They increasingly do so using information and communication technology (ICT) to communicate, coordinate their activities and to solve complex problems. One salient problem they face is how to effectively use requisite ICT tools. One important tool at their disposal is the self-help group, a body of people that organically spring up to solve shared problems. The more recognised term for this organisational form is a community of practice (COP). COPs generate knowledge networks that enhance and sustain competitive advantage and they are also used to help COP members actually use ICT tools. Etienne Wenger defines communities of practice as “groups of people informally bound together by shared expertise and passion for a joint enterprise” (Wenger and Snyder 2000, p139). This ‘chicken-or-egg’ issue about needing a COP to use the tools that are needed to effective broaden COPs (beyond co-located these groups) led us to explore how best to improve the process of ICT diffusion through construction organisations— primarily using people supported by technology that improves knowledge sharing. We present insights gained from recent PhD research results in this area. A semistructured interview approach was used to collect data from ICT strategists and users in the three large Australian construction organisations that are among the 10 or so first tier companies by annual dollar turnover in Australia. The interviewees were categorised into five organisational levels: IT strategist, implementer, project or engineering manager, site engineer and foreman. The focus of the study was on the organisation and the way that it implements ICT diffusion of a groupware ICT diffusion initiative. Several types of COP networks from the three Australian cases are identified: withinorganisation COP; institutional, implementer or technical support; project manager/engineer focussed; and collegial support. Also, there are cross-organisational COPs that organically emerge as a result of people sharing an interest or experience in something significant. Firstly, an institutional network is defined as a strategic group, interested in development of technology innovation within an organisation. This COP principally links business process domain experts with an ICT strategist.

Factors affecting ICT diffusion in Australian construction organisations – the storey from the big end

Our survey findings confirm that 11 factors influence information and communication technology (ICT) diffusion for experienced ICT users. We offer a model that consists of 4 groups of categories: management (M); individual (I); technology (T); and environment (E). Our conclusions reinforce the importance of a coherent ICT diffusion strategy and supportive environment. This requires substantial investment in training and collegial learning support mechanisms. This paper provides an overview of the work undertaken and an analysis of its implications for the construction industry and we provide useful insights that a wide range of construction industry professionals and contractors may find useful.

Bringing academics on board : encouraging institution-wide diffusion of e-learning environments

Rapid advances in educational and information communications technology (ICT)have encouraged some educators to move beyond traditional face to face and distance education correspondence modes toward a rich, technology mediated e-learning environment. Ready access to multimedia at the desktop has provided the opportunity for educators to develop flexible, engaging and interactive learning resources incorporating multimedia and hypermedia. However, despite this opportunity, the adoption and integration of educational technologies by academics across the tertiary sector has typically been slow. This paper presents the findings of a qualitative study that investigated factors influencing the manner in which academics adopt and integrate educational technology and ICT. The research was conducted at a regional Australian university, the University of Southern Queensland (USQ), and focused on the development of e-learning environments. These e-learning environments include a range of multimodal learning objects and multiple representations of content that seek to cater for different learning styles and modal preferences, increase interaction, improve learning outcomes, provide a more inclusive and equitable curriculum and more closely mirror the on campus learning experience. This focus of this paper is primarily on the barriers or inhibitors academics reported in the study, including institutional barriers, individual inhibitors and pedagogical concerns. Strategies for addressing these obstacles are presented and implications and recommendations for educational institutions are discussed.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.