A fast algorithm for the evaluation of Legendre expansions
SIAM Journal on Scientific and Statistical Computing
The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
SIAM Journal on Scientific Computing
Pseudospectral Legendre-based optimal computation of nonlinear constrained variational problems
Journal of Computational and Applied Mathematics
Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws
SIAM Journal on Numerical Analysis
Spectral methods in MatLab
Spectral method for constrained linear-quadratic optimal control
Mathematics and Computers in Simulation
Mathematical Programming: Series A and B
Hi-index | 0.00 |
In this paper, we derive the so-called Chebyshev-Legendre method for a class of optimal control problems governed by ordinary differential equations. We use Legendre expansions to approximate the control and state functions and we employ the Chebyshev-Gauss-Lobatto (CGL) points as the interpolating points. Thus the unknown variables of the equivalent nonlinear programming problems are the coefficients of the Legendre expansions of both the state and the control functions. We evaluate the function values at the CGL nodes via the fast Legendre transform. In this way, the fast Legendre transform can be utilized to save CPU calculation time. Some numerical examples are given to illustrate the applicability and high accuracy of the Chebyshev-Legendre method in solving a wide class of optimal control problem.