Numerical solutions of neutral stochastic functional differential equations

This paper examines the numerical solutions of neutral stochastic functional differential equations (NSFDEs) $d[x(t)-u(x_t)]=f(x_t)dt+g(x_t)dw(t)$, $t\geq 0$. The key contribution is to establish the strong mean square convergence theory of the Euler-Maruyama approximate solution under the local Lipschitz condition, the linear growth condition, and contractive mapping. These conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here are obtained under quite general conditions. Although the way of analysis borrows from [X. Mao, LMS J. Comput. Math., 6 (2003), pp. 141-161], to cope with $u(x_t)$, several new techniques have been developed

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A triangulation approach for design research

Triangulation has been adopted in social science in the study of the same phenomenon through applying and combining several data sources, research methods, investigators, and theoretical schemes. From a post-positivism view point, this paper presents a triangulation approach in design research from two perspectives, data sources and research methods. Data triangulation was achieved through collecting data from multiple sources including company design documents, student design projects, and company design projects. Different research methods, e.g. interview, content analysis, protocol analysis, and questionnaire, were used to conduct data collection and analysis into a particular aspect of design, the nature of coupling design artefact and process knowledge. It was found that triangulation can provide an effective means for design research

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