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Collocation Methods for Second Order Systems
Robotics: Science and Systems XVIII, 2022 Collocation methods for numerical optimal control commonly assume that the system dynamics is expressed as a first order ODE of the form x¿ = f(x, u, t), where x is the state and u the control vector. However, in many systems in robotics, the dynamics adopts the second order form q¨ = g(q, q¿, u, t), where q is the configuration.
Moreno Martín, Siro +2 more
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A Survey on Isogeometric Collocation Methods with Applications
Mathematics, 2023 Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin and collocation formulations. Exploiting
Jingwen Ren, Hongwei Lin
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Convergence rate for a Gauss collocation method applied to unconstrained optimal control
, 2015 A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem.
Hager, William W. +2 more
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A M\"untz-Collocation spectral method for weakly singular volterra integral equations [PDF]
, 2019 In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu ...
Azaiez, Mejdi +3 more
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Journal of King Saud University: Engineering Sciences, 2008 In this work we present a new numerical scheme based on orthogonal collocation method to solve a reacting flow problem. The method is based on recasting the problem to become a larger set of first order differential equations and we show by numerical ...
Moustafa A. Soliman, Khalid Alhumaizi
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Simple and accurate approach for solving of nonlinear heat convective-radiative equation in fin by using the collocation method and comparison with HPM and VIM [PDF]
Theoretical and Applied Mechanics, 2014 Collocation Method (CM) such as analytical technique, which does not need small parameters is here used to evaluate the analytical approximate solutions of the nonlinear heat transfer equation.
Rahimi Petroudi I. +4 more
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Sinc-Integral method to solve the linear Schrodinger equation [PDF]
Mathematics and Computational Sciences, 2020 The integral equation method is presented to solve the linear Schrodinger equation and obtain the eigenvalues. The eigenvalues obtained through this method are compared with Sinc-Collocation method.
Seyed Mohammad Ali Aleomraninjad +1 more
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Multi-quadric collocation model of horizontal crustal movement [PDF]
Solid Earth, 2016 To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used.
G. Chen, A. Zeng, F. Ming, Y. Jing
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On $hp$-Convergence of PSWFs and A New Well-Conditioned Prolate-Collocation Scheme
, 2013 The first purpose of this paper is to provide a rigorous proof for the nonconvergence of $h$-refinement in $hp$-approximation by the PSWFs, a surprising convergence property that was first observed by Boyd et al [J. Sci. Comput., 2013].
Wang, Li-Lian +2 more
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Stability of Chebyshev collocation methods
Computers & Mathematics with Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
COSTABILE F, NAPOLI, Anna
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