title: Forward Period Analysis Method of the Periodic Hamiltonian System.
abstract: Using the forward period analysis (FPA), we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term [0, 1060] (time unit) solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series (PMT) scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested.
authors.affiliation: State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China.|Center for Monsoon System Research, Institute of Atmospheric Physics (CMSR), Chinese Academy of Sciences, Beijing, China.
authors.forename: Pengfei
authors.initials: P
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D008433:Mathematics; D011897:Random Allocation