In this paper, explicit Runge–Kutta methods are investigated for numerical solutions of nonlinear dynamical systems with conserved quantities. The concept, ε-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 the 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.
A Modified Runge–Kutta Method for Nonlinear Dynamical Systems With Conserved Quantities
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 28, 2016; final manuscript received May 10, 2017; published online July 12, 2017. Assoc. Editor: Haiyan Hu.
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Hu, G. (July 12, 2017). "A Modified Runge–Kutta Method for Nonlinear Dynamical Systems With Conserved Quantities." ASME. J. Comput. Nonlinear Dynam. September 2017; 12(5): 051026. https://doi.org/10.1115/1.4036761
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