A METHOD SOLVING KEPLERS EQUATION WITHOUT TRANSCENDENTAL FUNCTION EVALUATIONS

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for th e elliptic case. The resulting method requires no evaluation of transc endental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fas t as Halley's method, Nijenhuis's method, and others.