Nonlinear Differential Equation Solvers via Adaptive Picard–Chebyshev Iteration: Applications in Astrodynamics
An adaptive self-tuning Picard-Chebyshev numerical integration method is presented for solving initial and boundary value problems by considering high-fidelity perturbed two-body dynamics. The current adaptation technique is self-tuning and adjusts the size of the time interval segments and the numb...
Gespeichert in:
Veröffentlicht in: | Journal of guidance, control, and dynamics control, and dynamics, 2019-05, Vol.42 (5), p.1007-1022 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | An adaptive self-tuning Picard-Chebyshev numerical integration method is presented for solving initial and boundary value problems by considering high-fidelity perturbed two-body dynamics. The current adaptation technique is self-tuning and adjusts the size of the time interval segments and the number of nodes per segment automatically to achieve near-maximum efficiency. The technique also uses recent insights on local force approximations and adaptive force models that take advantage of the fixed-point nature of the Picard iteration. In addition to developing the adaptive method, an integral quasi-linearization "error feedback- term is introduced that accelerates convergence to a machine precision solution by about a of two. The integral quasi linearization can be implemented for both first- and second-order systems of ordinary differential equations. A discussion is presented regarding the subtle but significant distinction between integral quasi linearization for first-order systems, second-order systems that can be rearranged and integrated in first-order form, and second-order systems that are integrated using a kinematically consistent Picard-Chebyshev iteration in cascade form. The enhanced performance of the current algorithm is demonstrated by solving an important problem in astrodynamics: the perturbed two-body problem for near-Earth orbits. The adaptive algorithm has proven to be more efficient than an eighth-order Gauss-Jackson and a 12th/10th-order Runge-Kutta while maintaining machine precision over several weeks of propagation. |
---|---|
ISSN: | 0731-5090 1533-3884 |
DOI: | 10.2514/1.G003318 |