0
research-article

A Modified Runge-Kutta Method for Nonlinear Dynamical Systems with Conserved Quantities

[+] Author and Article Information
Guang-Da Hu

Professor, Department of Mathematics Shanghai University, Shanghai, 200444, China
ghu@hit.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4036761 History: Received November 28, 2016; Revised May 10, 2017

Abstract

In this paper, explicit Runge-Kutta methods are investigated for numerical solutions of nonlinear dynamical systems with conserved quantities. The concept, $\varepsilon-$preserving is introduced to describe the conserved quantities being approximately retained. Then a modified version of explicit Runge-Kutta methods based on the optimization technique is presented. With respect to the computational effort, the modified Runge-Kutta method is superior to implicit numerical methods in literature. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in preserving the conserved quantities to the standard one. Numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.

Copyright (c) 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In