naa a22 4500 510774261 CHVBK 20180411083225.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1007/s40295-015-0061-1 doi (NATIONALLICENCE)springer-10.1007/s40295-015-0061-1 Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics [Elektronische Daten] [John Junkins, Ahmad Bani Younes, Robyn Woollands, Xiaoli Bai] This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics. Using Chebyshev polynomials, as the orthogonal approximation basis, it is straightforward to distribute the computation of force functions needed in MCPI to generate the polynomial coefficients (approximating the path iterations) to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refines path estimates over large time intervals chosen to be within the domain of convergence of Picard iteration. The developed vector-matrix form makes MCPI methods computationally efficient and a more systematic approach is given, leading to a modest correction to results in the published dissertation by Bai. The power of MCPI methods for solving IVPs is clearly illustrated using a simple nonlinear differential equation with a known analytical solution. Compared with the most common integration scheme, the standard Runge-Kutta 4-5 method as implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, on a serial machine. MCPI performance is also compared to state of the art integrators such as the Runge-Kutta Nystrom 12(10) methods applied to the relevant orbit mechanics problems. The MCPI method is shown to be well-suited to solving these problems in serial processors with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. When used in conjunction with the recently developed local gravity approximations in conjunction with parallel computation, we anticipate MCPI will enable revolutionary speedups while ensuring accuracy. American Astronautical Society, 2015 Picard iteration nationallicence Chebyshev polynomials nationallicence Initial value problems nationallicence Orbit propagation nationallicence Junkins John Aerospace Engineering Department, Texas A & M University, 722 H.R. Bright Building, 3141 TAMU, 77843-3141, College Station, TX, USA aut Bani Younes Ahmad Aerospace Engineering Department, Khalifa University, Abu Dhabi, United Arab Emirates aut Woollands Robyn Aerospace Engineering Department, Texas A & M University, 701 H.R. Bright Building, 3141 TAMU, 77843-3141, College Station, TX, USA aut Bai Xiaoli Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Rd., EN B-222, 08854, Piscataway, NJ, USA aut The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 623-653 0021-9142 60:3-4<623 2013 60 40295 https://doi.org/10.1007/s40295-015-0061-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s40295-015-0061-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Junkins John Aerospace Engineering Department, Texas A & M University, 722 H.R. Bright Building, 3141 TAMU, 77843-3141, College Station, TX, USA aut NATIONALLICENCE 700 1- Bani Younes Ahmad Aerospace Engineering Department, Khalifa University, Abu Dhabi, United Arab Emirates aut NATIONALLICENCE 700 1- Woollands Robyn Aerospace Engineering Department, Texas A & M University, 701 H.R. Bright Building, 3141 TAMU, 77843-3141, College Station, TX, USA aut NATIONALLICENCE 700 1- Bai Xiaoli Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, 98 Brett Rd., EN B-222, 08854, Piscataway, NJ, USA aut NATIONALLICENCE 773 0- The Journal of the Astronautical Sciences Springer US; http://www.springer-ny.com 60/3-4(2013-12-01), 623-653 0021-9142 60:3-4<623 2013 60 40295 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer