The Study of Accuracy and Efficiency of ODE Solvers While Performing Numerical Simulations of Terrestrial Planets
The Study of Accuracy and Efficiency of ODE Solvers
Keywords:
Kepler’s two body problem, N-body simulations, Terrestrial planets, ODE solversAbstract
The N-body problem is one of the well-known and most central computational problem. The N-body problem of the Solar System is not only a rich source of initial value problems (IVPs) for ordinary differential equations (ODEs), but is also very convenient to understand the orbital evolution of the Solar System; see, for example,[1, 2]. Wide range of numerical integrators have been developed and implemented for performing such N-body simulations. The main objective of this research paper is to analyze and compare the accuracy and efficiency of different ordinary differential equation (ODE) solvers applied to the Kepler’s two-body problem for Terrestrial planets. Throughout this paper, the error growth is investigated in terms of global error in position and velocity, and the relative error in terms of angular momentum and total energy of the system. To quantify the quality of different ODE solvers, we performed numerical tests applied to the Kepler’s two body problem for Terrestrial planets with local error tolerances ranging from 10−12 to 10−4.
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