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DQ Based Methods: Theory and Application to Engineering and Physical Sciences
Abstract
Though relatively unknown, the Differential Quadrature Method (DQM) is a promising numerical technique that produces accurate solutions with less computational effort than other numerical methods such as the Finite Element Method. There are different versions of the former method, so one can refer to a class of methods based on the differential quadrature (DQ) approach. This chapter provides systematic steps to understand DQ based methods: how they work, how to use and develop them, as well as exemplary problems. It is divided into two sections: the first provides fundamentals and theories related to the DQ approach, while the second presents the application of DQ based methods to three significant problems, i.e. free vibrations of a multi-span beam (a typical model for bridge decks and floors), time dependent heat transfer, and vibrations of a rectangular membrane. The main focus is on the application of the method to space-time domains as a whole, an issue not well covered by the current literature.
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