This paper presents a class of efficient Newton-type algorithms for solving the nonlinear programs (NLPs) arising from applying a direct collocation approach to continuous time optimal control. The idea is based on an implicit lifting technique including a condensing and expansion step, such that the structure of each subproblem corresponds to that of the multiple shooting method for direct opt...

Among fitted-operator methods for solving one-dimensional singular perturbation problems one of the most accurate is the collocation by linear combinations of {1, x, exp (±px)}, known as tension spline collocation. There exist well established results for determining the ‘tension parameter’ p, as well as special collocation points, that provide higher order local and global convergence rates. H...

We performed a comparison between the interpolation methods of Kriging and Least Squares Collocation. This allowed to obtain an optimal velocity model earth’s crust for continental Ecuador from field ITRF2008 obtained with GNSS data in period 2008-2014. The best fitting semivariograms two components were Spherical Stable semivariogram. functional Collocation method was third order East componen...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

The Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA and MATLAB). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum,...

In this paper, we propose a Modified nested sparse grid based Adaptive Stochastic Collocation Method (MASCM) for block-based Statistical Static Timing Analysis (SSTA). The proposed MASCM employs an improved adaptive strategy derived from the existing Adaptive Stochastic Collocation Method (ASCM) to approximate the key operator MAX during timing analysis. In contrast to ASCM which uses non-neste...