This paper proposes a second-order scheme of precision integration for dynamic analysis with respect to long-term integration. Rather than transforming into first-order equations, a recursive scheme is presented in detail for direct solution of the homogeneous part of second-order algebraic and differential equations. The sine and cosine matrices involved in the scheme are calculated using the so-called 2Nalgorithm. Numerical tests show that both the efficiency and the accuracy of homogeneous equations can be improved considerably with the second-order scheme. The corresponding particular solution is also presented, incorporated with the second-order scheme where the excitation vector is approximated by the truncated Taylor series. © 2005 Elsevier Ltd. All rights reserved.
Ma, H., & Qin, Q. H. (2005). A second-order scheme for integration of one-dimensional dynamic analysis. Computers and Mathematics with Applications, 49(2–3), 239–252. https://doi.org/10.1016/j.camwa.2004.08.009