Journal of Applied Mathematics

An Energy Conservation Algorithm for Nonlinear Dynamic Equation

Jian Pang, Yu Du, Ping Hu, Weidong Li, and Z. D. Ma

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 453230, 18 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479347

Digital Object Identifier
doi:10.1155/2012/453230

Mathematical Reviews number (MathSciNet)
MR2880826

Zentralblatt MATH identifier
1235.65076

Citation

Pang, Jian; Du, Yu; Hu, Ping; Li, Weidong; Ma, Z. D. An Energy Conservation Algorithm for Nonlinear Dynamic Equation. J. Appl. Math. 2012 (2012), Article ID 453230, 18 pages. doi:10.1155/2012/453230. https://projecteuclid.org/euclid.jam/1350479347


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