Symplectic waveform relaxation methods for Hamiltonian systems

In this literature, a new method called symplectic waveform relaxation method is for the first time proposed to solve Hamiltonian systems. This method is based on waveform relaxation method which makes computation cheaper, and makes use of symplectic method to determine its numerical scheme. Under the guidance of the symplectic method, the discrete waveform relaxation method elegantly preserves the discrete symplectic form. Windowing technique is utilized to accelerate computation. The windowing technique also makes it possible to advance in time, window by window. Convergence results of continuous and discrete symplectic waveform relaxation methods are analyzed. Numerical results show that the symplectic waveform relaxation method with the windowing technique precisely preserves the Hamiltonian function.