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.

Extending conceptual models for Web based applications

The next phase envisioned for the World Wide Web is automated ad-hoc interaction between intelligent agents, web services, databases and semantic web enabled applications. Although at present this appears to be a distant objective, there are practical steps that can be taken to advance the vision. We propose an extension to classical conceptual models to allow the definition of application components in terms of public standards and explicit semantics, thus building into web-based applications, the foundation for shared understanding and interoperability. The use of external definitions and the need to store outsourced type information internally, brings to light the issue of object identity in a global environment, where object instances may be identified by multiple externally controlled identification schemes. We illustrate how traditional conceptual models may be augmented to recognise and deal with multiple identities.