A Second-order Time-marching Procedure with Enhanced Accuracy
Delfim Soares Jr.

doi:10.3970/cmes.2015.105.341
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 105, No. 5, pp. 341-360, 2015
Download Full length paper in PDF format. Size = 2,024,913 bytes
Keywords Time Integration Methods, Trapezoidal Rule, Central Difference Method, Stability, Accuracy, Period Elongation Errors.
Abstract

In this work, a second-order time-marching procedure for dynamics is discussed, in which enhanced accuracy is enabled. The new technique is unconditionally stable (according to its parameter selection), it has no amplitude decay or overshooting, and it provides reduced period elongation errors. The method is based on displacement-velocity relations, requiring no computation of accelerations. It is efficient, simple and very easy to implement. Numerical results are presented along the paper, illustrating the good performance of the proposed technique. As it is described here, the new method has no drawbacks when compared to the Trapezoidal Rule (TR), which is one of the most popular time-marching techniques in dynamics, being always more accurate than the TR.

PDF download PDF