A comparison is made between three pseudospectral methods used to numerically solve optimal control problems. In particular, the accuracy of the state, control, and costate obtained using the Legendre, Radau, and Gauss pseudospectral methods is compared. Three examples with different degrees of complexity are used to identify key differences between the three methods. The results of this study ...

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic–acoustic, and electromagnetic wave propagation. Our analytical results are developed for both conforming and non-conforming approximations on hexahedral meshes using either exact integration with Legendr...

A new approach to the numerical solution of systems of first-order ordinary differential equations is given by finding local Galerkin approximations on each subinterval of a given mesh of size h. One step at a time, a piecewise polynomial, of degree n and class C°, is constructed, which yields an approximation of order 0(A*") at the mesh points and 0(A"+1) between mesh points. In addition, the ...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...

Different discretization and trust-region methods are compared for the low-thrust fuel-optimal trajectory optimization problem using successive convex programming. In particular, differential integral formulations of adaptive pseudospectral Legendre–Gauss–Radau method, an arbitrary-order Legendre–Gauss–Lobatto technique based on Hermite interpolation, a first-order-hold considered. The number p...

where p (> 3) is a rational prime such that p ≡ 3 (mod 4) and p ≡ 1 (mod 4), respectively ; ( p ) is the Legendre symbol and h(−p) is the class number of the quadratic field Q( √−p). The formulas are apparently related to the Dirichlet L-values at s = 1. To get a typical elliptic Gauss sum, we have only to replace the Legendre symbol by the cubic or the quartic residue character, and the trigon...

We propose a two algorithms for computation of (sharp) enclosures of definite interevals: a lor.rd adaptive dgorid~a (LAA) and a g/oba/ a&,pth~ cdgor92~n (GAA). Both algorithms are based (m Gauss-Legendre ~ladrature. Error terms are bounded using automatic differentiation in combination with interval evah:adons. Several nmnerical examples are presented; these examples include comparis~m with an...

We compute point sets on the triangle that have low Lebesgue constant, with sixfold symmetries and Gauss-Legendre-Lobatto distribution on the sides, up to interpolation degree 18. Such points have the best Lebesgue constants among the families of symmetric points used so far in the framework of triangular spectral elements.