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...

This paper describes a simple but effective technique for reducing dispersion errors in finite element solutions of timeharmonic wave propagation problems. The method involves a simple shift of the integration points to locations away from conventional Gauss or Gauss–Lobatto integration points. For bilinear rectangular elements, such a shift results in fourth-order accuracy with respect to disp...

In this article, a shifted Legendre tau method is introduced to get a direct solution technique for solving multi-order fractional differential equations (FDEs) with constant coefficients subject to multi-point boundary conditions. The fractional derivative is described in the Caputo sense. Also, this article reports a systematic quadrature tau method for numerically solving multi-point boundar...

This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as points and derived differentiation matrices for derivatives. With matrices, were transformed into linear systems, which are easier solve. Two types of numerical simulations, results demo...

In this paper, we examine the influence of numerical integration on finite element methods using quadrilateral or hexahedral meshes in the time domain. We pay special attention to the use of Gauss-Lobatto points to perform mass lumping for any element order. We provide some theoretical results through several error estimates that are completed by various numerical experiments. c © ??? John Wile...

We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes which elements mimic as well as possible the Chebyshev-Loba...