An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems

作者：Miyatake Yuto^*

来源：BIT Numerical Mathematics, 2014, 54(3): 777-799.

DOI：10.1007/s10543-014-0474-4

• Continuous stage Runge-Kutta method
• Energy-preservation
• Exponential fitting
• Hamiltonian systems

Recently, the symplectic exponentially-fitted methods for Hamiltonian systems with periodic or oscillatory solutions have been attracting a lot of interest. As an alternative to them, in this paper, we propose a class of energy-preserving exponentially-fitted methods. For this aim, we show sufficient conditions for energy-preservation in terms of the coefficients of continuous stage Runge-Kutta (RK) methods, and extend the theory of exponentially-fitted RK methods in the context of continuous stage RK methods. Then by combining these two theories, we derive second and fourth order energy-preserving exponentially-fitted schemes.

• 出版日期2014-9