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Higher-order Derivatives (higher-order + derivative)
Selected AbstractsOptimal Control of Rigid-Link Manipulators by Indirect MethodsGAMM - MITTEILUNGEN, Issue 1 2008Rainer Callies Abstract The present paper is a survey and research paper on the treatment of optimal control problems of rigid-link manipulators by indirect methods. Maximum Principle based approaches provide an excellent tool to calculate optimal reference trajectories for multi-link manipulators with high accuracy. Their major drawback was the need to explicitly formulate the complicated system of adjoint differential equations and to apply the full apparatus of optimal control theory. This is necessary in order to convert the optimal control problem into a piecewise defined, nonlinear multi-point boundary value problem. An accurate and efficient access to first- and higher-order derivatives is crucial. The approach described in this paper allows it to generate all the derivative information recursively and simultaneously with the recursive formulation of the equations of motion. Nonlinear state and control constraints are treated without any simplifications by transforming them into sequences of systems of linear equations. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An improved meshless collocation method for elastostatic and elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008P. H. Wen Abstract Meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. In this paper, an improved meshless collocation method is presented for use with either moving least square (MLS) or compactly supported radial basis functions (RBFs). A new technique referred to as an indirect derivative method is developed and compared with the direct derivative technique used for evaluation of second-order derivatives and higher-order derivatives of the MLS and RBF shape functions at the field point. As the derivatives are obtained from a local approximation (MLS or compact support RBFs), the new method is computationally economical and efficient. Neither the connectivity of mesh in the domain/boundary nor integrations with fundamental/particular solutions is required in this approach. The accuracy of the two techniques to determine the second-order derivative of shape function is assessed. The applications of meshless method to two-dimensional elastostatic and elastodynamic problems have been presented and comparisons have been made with benchmark analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] A Cartesian grid technique based on one-dimensional integrated radial basis function networks for natural convection in concentric annuliINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008N. Mai-Duy Abstract This paper reports a radial basis function (RBF)-based Cartesian grid technique for the simulation of two-dimensional buoyancy-driven flow in concentric annuli. The continuity and momentum equations are represented in the equivalent stream function formulation that reduces the number of equations from three to one, but involves higher-order derivatives. The present technique uses a Cartesian grid to discretize the problem domain. Along a grid line, one-dimensional integrated RBF networks (1D-IRBFNs) are employed to represent the field variables. The capability of 1D-IRBFNs to handle unstructured points with accuracy is exploited to describe non-rectangular boundaries in a Cartesian grid, while the method's ability to avoid the reduction of convergence rate caused by differentiation is instrumental in improving the quality of the approximation of higher-order derivatives. The method is applied to simulate thermally driven flows in annuli between two circular cylinders and between an outer square cylinder and an inner circular cylinder. High Rayleigh number solutions are achieved and they are in good agreement with previously published numerical data. Copyright © 2007 John Wiley & Sons, Ltd. [source] The Production Responses of the Competitive Firm to Three Conventional Distributional Shifts: a Unified PerspectiveMETROECONOMICA, Issue 2 2000Wayne Simpson This paper presents a unified perspective on the production responses of the competitive firm to three conventional distributional shifts: (i) a rightward shift of the distribution, (ii) a Rothschild,Stiglitz increase in risk, and (iii) a Menezes et al. increase in downside risk. In particular, assuming that the von Neumann,Morgenstern utility is increasing and concave, and assuming its higher-order derivatives are uniformly signed, we demonstrate that the production responses are unambiguous in the case of price less than or equal to marginal cost. In the alternative case of price greater than marginal cost, we then demonstrate that the production responses can be signed unambiguously by reference to sufficient conditions motivated by absolute risk aversion and by absolute prudence. [source] | ||||||||||