Based on Lagrange and Hermite interpolation two novel versions of weak form quadrature element are proposed for a non-classical Euler-Bernoulli beam theory. By extending these concept two new plate elements are formulated using Lagrange-Lagrange and mixed Lagrange-Hermite interpolations for a non-classical Kirchhoff plate theory. The non-classical theories are governed by sixth order partial di...

In this study, we consider ill-posed time-domain inverse problems for dynamical systems with various boundary conditions and unknown controllers. Dynamical systems characterized by a system of second-order nonlinear ordinary differential equations (ODEs) are recast into a system of nonlinear first order ODEs in mixed variables. Radial Basis Functions (RBFs) are assumed as trial functions for th...

In this paper, we investigate the stability of a numerical method for solving wave equation. The uses explicit leap-frog in time and high order continuous discontinuous (DG) finite elements using standard Lagrange Hermite basis functions space. Matrix eigenvalue analysis is used to calculate time-step restrictions. We show that restriction independent nodal distribution, such as equidistributed...

In this paper, we present and study \begin{document}$ C^1 $\end{document} Petrov-Galerkin Gauss collocation methods with arbitrary polynomial degree id="M3">\begin{document}$ k (\begin{document}$ \ge 3 $\end{document}) for one-dimen\-sional ell...

In this paper, a linear Chebyshev pseudospectral method (LCPM) is proposed to solve the nonlinear optimal control problems (OCPs) with hard terminal constraints and unspecified final time, which uses collocation scheme quasi-linearization. First, Taylor expansion around differential equations of system used obtain set perturbation equations. Second, first-order necessary conditions for OCPs the...

Abstract In this paper we discuss the use of implicit Runge–Kutta schemes for time discretization optimal control problems with evolution equations. The specialty considered discretizations is that state and adjoint are chosen such optimization commute. It well known property additional order conditions necessary. We give sufficient which class these condition automatically fulfilled. focus esp...

Superconvergence phenomenon of the Legendre spectral collocation method and the p-version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): ‖u‖L∞ ≤ cMk on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is supergeometric. Furthermore, at proper Gaussia...