An Energy Conservation Algorithm for Nonlinear Dynamic Equation
Joint Authors
Ma, Z.-D.
Pang, Jian
Du, Yu
Hu, Ping
Li, Weidong
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-09
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed.
Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved.
However, this formula still includes a parameter that is to be determined.
Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter.
Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula.
Several examples are used to compare the current method with the well-known Runge-Kutta method.
They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.
American Psychological Association (APA)
Pang, Jian& Du, Yu& Hu, Ping& Li, Weidong& Ma, Z.-D.. 2012. An Energy Conservation Algorithm for Nonlinear Dynamic Equation. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-993266
Modern Language Association (MLA)
Pang, Jian…[et al.]. An Energy Conservation Algorithm for Nonlinear Dynamic Equation. Journal of Applied Mathematics No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-993266
American Medical Association (AMA)
Pang, Jian& Du, Yu& Hu, Ping& Li, Weidong& Ma, Z.-D.. An Energy Conservation Algorithm for Nonlinear Dynamic Equation. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-993266
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993266