Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems

.It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of the problems and the requirement of highly stable and energy-preserving schemes. The previously constructed numerical schemes are generally fully implicit and thus result in a considerable computational cost in long-time integrations. In this paper, a family of explicit and energy-conserving schemes are presented for solving oscillatory Hamiltonian systems. These schemes are developed by using the idea of the construction of exponential Rosenbrock-type (ER) methods and relaxation techniques. The novel relaxation methods can be high-order accurate and have better long-time numerical behavior than the corresponding ER methods. Several numerical experiments on typical models are given to demonstrate the efficiency of the proposed methods.Keywordsoscillatory Hamiltonian systemsexponential Rosenbrock-type methodsrelaxation parameterhigh-order accuracyconservationstabilityMSC codes65L0465L0665M12