Abstract. We introduce the Shepard-Bernoulli operator as a combination of the Shepard operator with a new univariate interpolation operator: the generalized Taylor polynomial. Some properties and the rate of convergence of the new combined operator are studied and compared with those given for classical combined Shepard operators. An application to the interpolation of discrete solutions of initial value problems is given.

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Purpose -This paper aims to provide a relevant backdrop for the Worldwide Hospitality and Tourism Themes (WHATT) theme issue on the hotel industry of Canada, and to describe how the 2012 WHATT roundtable in Canada was organised. Design/methodology/approach -The foundation for this paper was laid during a well attended Worldwide Hospitality and Tourism Themes (WHATT) roundtable discussion between industry leaders and hospitality educators in May 2012. The paper is written in the context of the theme and strategic question for the 2012 Canadian WHATT roundtable: "What innovations are needed in the Canadian hotel industry and how might they be implemented to secure the industry's future?". Findings -This paper provides key information on Canada, its economic conditions, the tourism industry and the hotel industry. It also explains the origins of WHATT and its scholarly journey over the last 19 years. In capturing the essence of the 2012 WHATT roundtable discussion in Canada, the paper provides a strong foundation for the other seven papers that follow in this WHATT theme issue. Practical implications -The paper looks at key challenges of the hotel industry in Canada and provides thought-provoking viewpoints from experts. Originality/value -Readers who are interested in the Canadian hotel industry would benefit from this paper. Authors include the president of the umbrella trade association for the hotel industry, the Hotel Association of Canada, and the editor and publisher of the leading trade magazine for the hotel industry of Canada, Hotelier.

Abstract.This paper develops a general theory for a class of Runge-Kutta methods which are based, in addition to the stages of the current step, also on the stages of the previous step. Such methods have been introduced previously for the case of one and two stages. We show that for any number s of stages methods of order p with s + 1 < p < 2s can be constructed. The paper terminates with a study of step size change and stability.

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