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Keywords:
energy-preserving; explicit Runge–Kutta methods; gradient
energy-preserving; explicit Runge–Kutta methods; gradient
Summary:
In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments are provided to illustrate the effectiveness of the modified Runge-Kutta method.
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