Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Introducing ethnomethodological analysis to the field of music education

In recent years qualitative research methods have been adopted within in the field of music education and have received widespread acceptance. However, the theoretical framework provided by ethnomethodology (Garfinkel, 1974, in R. Turner, Ethnomethodology , Penguin, Middlesex, UK) and the tools of conversational analysis (Sacks, 1992, Lectures on Conversation , edited by Gail Jefferson, Blackwell, Oxford, UK) have, to this point, been overlooked by researchers in the field of music education. In this paper I argue that the application of ethnomethodological and conversation analytical approaches in the field of research in music education can provide fresh insights into the work of music teachers and how this work is accomplished in institutional settings. Here I demonstrate how a conversation analytical perspective drawing on an ethnomethodological framework might be used to investigate transcripts of audio-recorded interview talk. This type of analysis can illuminate aspects of members' roles in relation to, and perceptions about music education in school settings that might be overlooked in other types of analysis. A conversation analytical approach to the examination of talk-in-interaction explicates in fine-grained detail how members orient to matters at hand in the context of research settings, as well as revealing features of the cultural world of music teaching. Further application of the approach to research problems in other school settings, I argue, will inform the field of music education in ways yet to be realised.

Domestic objects and the taste epiphany - A resource for consumption methodology

The presentation of an aesthetic identity involves the accomplishment of a coherent, plausible narrative which links one's choices to desired characteristics of the self. As symbolic evidence of a person's taste, material culture is a vital component of a successful narrative. Via case studies of pivotal household objects, this paper uses face-to-face interview data as a way of investigating processes of aesthetic choice. Household objects are interpreted as material elements imbricated in the presentation of a socially plausible and internally consistent aesthetic self. Narrative analysis, and the concept of the epiphany-object, are proposed as useful ways of accounting for tastes in domestic material culture. Methodological questions of truth-telling and authenticity in the face-to-face context are considered, and the sociological problem of taste is scrutinized in light of ideas about social accountability and textual identity.