A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

Shuai Zhu, Gang Zhou, Xiaomei Liu, Shilie Weng, P. Plapper, M. Guo, S. Suhag
2016 MATEC Web of Conferences  
Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case wh ich the system is badly stiff. High Precision Direct integration based on variational principle is given (HP D-VP) for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is m uch
more » ... which is m uch precise an d is stiff A-stable, but also can avoid the truncation error of the computer. For the large systems, especially, the systems with different frequency or the stiff systems, our methods are stable, accurate and efficient. Numerical experiments show the convergence order of the scheme derived from the variational principle, and is much precise and is effective in engineering.
doi:10.1051/matecconf/20164205002 fatcat:eet52vqwkffvbjpsipell5cafq