On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms

In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.

AN EXPLICIT HIGH ORDER PREDICTOR-CORRECTOR METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

An explicit Runge-Kutta type method is developed here. This method has an algebraic order six, a large interval of periodicity and a phase-lag of order eight. It is much more efficient than other well known methods when applying to an orbit equation.