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Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions

Yousef Edrisi Tabriz, Mehrdad Lakestani (2015)

Kybernetika

In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative ( 𝐃 φ ) and integration matrix ( 𝐏 ) are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...

Discrete evolutions: Convergence and applications

Erich Bohl, Johannes Schropp (1993)

Applications of Mathematics

We prove a convergence result for a time discrete process of the form x ( t + h ) - x ( t ) = h V ( h , x ( t + α 1 ( t ) h ) , . . . , x ( t + α L ( t ) h ) ) t = T + j h , j = 0 , . . . , σ ( h ) - 1 under weak conditions on the function V . This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.

Discrete maximum principle for interior penalty discontinuous Galerkin methods

Tamás Horváth, Miklós Mincsovics (2013)

Open Mathematics

A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...

Driver's influence on kinematics of articulated bus rear axle

Bartoň, Stanislav, Krumphole, Tomáš (2013)

Programs and Algorithms of Numerical Mathematics

This paper studies kinematic properties of the rear axle of the particle coach as function of driver’s activity. The main goals are the prediction of the trajectory, the computation of the vector of velocity of each wheel of the rear axle as a function of the real velocity vector of the front coach axle and the real curvature of the bus trajectory. The computer algebra system MAPLE was used for all necessary computations.

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