State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

The halo orbits around the Earth-Moon L2 libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recentl...

Error Analysis for Picard-Chebyshev Iterations

The Chebyshev iteration revisited

Compared to Krylov space methods based on orthogonal or oblique projection, the Chebyshev iteration does not require inner products and is therefore particularly suited for massively parallel computers with high communication cost. Here, six different algorithms that implement this method are presented and compared with respect to roundoff effects, in particular, the ultimately achievable accur...

A Picard Iteration Based Integrator

converge to a unique solution of the IVP up to the boundary of U [1]. In general, φn may converge slowly to the exact solution. The Picard iteration based integrator described in this paper has three main advantages. The the integrator has arbitrary order, is time adaptive, and has dense output. Dense output refers to the integrator being able to take time steps of variable length without havin...

Chebyshev semi-iteration in Preconditioning

It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required then the Conjugate Gradient method will compute the optimal approximate solution from the appropriate Krylov subspace, that is, it will implicitly compute the optimal polynomial. ...