AN ADAPTIVE APPROACH FOR MODIFIED CHEBYSHEV PICARD ITERATION
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The demand of having fast and efficient numerical propagators to solve engineering problems has become essential. The level of system complexity increases the cost of obtaining the solution. Many real world problems require developing efficient, precise and fast solutions. For example, efficient, high precision orbit propagation has gained renewed impetus due to the rapidly escalating demands for improved Space Situational Awareness (SSA) and the challenges posed by the Kessler Syndrome, which hypothesizes that every collision of two space objects drastically increases the probability of subsequent collisions. The recent development Junkins et al. of Modiffed Chebyshev Picard Iteration (MCPI) has shown efficient solution for many engineering problems that require precise and fast solutions. This paper is an extension to various developments on MCPI by introducing an adaptive technique that enables the flexibility in the choice of the degree to approximate the trajectory and the force function. The proposed approach avoids the need to use the same number of nodes to approximate, both, the trajectory and the force function. This reduces the computation cost. In addition, the different choices of the approximation degree can be utilized to adapt the iteration process by tuning the approximation degree. The cost benefit of this approach depends strongly on the problem of interest. Some examples showed that a speed up of greater than 1.5X is achieved compared with the original MCPI approach.
