Multi-segment adaptive modified Chebyshev Picard iteration method

A modified Chebyshev Picard iteration method is proposed for solving orbit propagation initial value problems. Cosine sampling, known as Chebyshev-Gauss-Labatto (CGL) node, is used to reduce the Runge's phenomenon that plagues many series approximations. The key benefit of using the CGL data sampling is that the nodal points are distributed non-uniformly, with dense sampling at the beginning and end times. This problem can be addressed by a nonlinear time transformation and/or by utilizing multiple time segments over an orbit. This paper suggests a method, called a multi-segment method, to obtain accurate solutions overall regardless of initial positions and eccentricity by dividing the given orbit into two or more segments.

Multi-segment adaptive modified Chebyshev Picard iteration method Conference Paper