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...

In this paper, we extend the study of superconvergence properties of ChebyshevGauss-type spectral interpolation in [24, SINUM,Vol. 50, 2012] to general Jacobi-Gauss-type interpolation. We follow the same principle as in [24] to identify superconvergence points from interpolating analytic functions, but rigorous error analysis turns out much more involved even for the Legendre case. We address t...

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...