The extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of an offshore mechanics or arctic engineering problem. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of offshore mechanics and arctic problems by using a certain discretization technique such as the DQEM, FEM, FDM,…, etc.

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