Dimension reduction for second-order systems by general orthogonal polynomials

In this article, we discuss the time-domain dimension reduction methods for second-order systems by general orthogonal polynomials, and present a structure-preserving dimension reduction method for second-order systems. The resulting reduced systems not only preserve the second-order structure but also guarantee the stability under certain conditions. The error estimate of the reduced models is also given. The effectiveness of the proposed methods is demonstrated by three test examples.