Understanding the evolution of satellite orbits in the long-term is of great importance in astrodynamics. In order to achieve this, accurate propagation of the orbital dynamics of the satellite is required. This paper presents implementation and evaluation of a class of numerical integration methods known as symplectic algorithms. This class of algorithms is highly regarded in scientific applications, especially in long-term studies. The objective of this paper is to demonstrate the superior accuracy and efficient speed of several algorithms of this class and obtain long-term state of satellites under the several influencing forces. Within each application, several cases with different values for parameters such as the time step and duration are executed. In addition, long-term orbital evolution of a satellite in various orbital regimes is conducted. The results indicate that the symplectic algorithms are more accurate for orbit propagation at various time increments tested. In addition, the symplectic algorithms are more computationally efficient in all but a few cases.
