Abstract
This paper presents numerical solutions for relativistic dynamics by the Symplectic Integrator (SI) and Totally Conservative Integrator (TCI), and proposes Symmetric TCI (S-TCI) for improving the TCI. For some kinetic problems, the TCI is more efficient than the SI, e.g. faster calculation and higher accuracy. However, some inaccuracy results by the TCI for relativistic dynamics are indicated. To overcome its problem, time-reversal S-TCI is derived based on composition methods with the adjoint method. Numerical solutions by S-TCI show greatly improvement compared with the ordinary TCI.
