In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second appro...

Consider integration over the unit sphere in , especially when the integrand has singular behaviour in a polar region. In an earlier paper [4], a numerical integration method was proposed that uses a transformation that leads to an integration problem over the unit sphere with an integrand that is much smoother in the polar regions of the sphere. The transformation uses a grading parameter . Th...

We explore an intimate connection between Young tableaux and representations of the symmetric group. We describe the construction of Specht modules which are irreducible representations of Sn, and also highlight some interesting results such as the branching rule and Young’s rule.

Following the ideas of Liniger and Willoughby (although acting along different lines), a new family of schemes, derived from the trapezoidal rule, is developed, which enables the fitting of the scheme to arbitrary sets of equations.

In this paper, we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval. Then, we find the best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval. Finally, we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected int...

This article presents a particle method framework for simulating molecular dynamics. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. Error estimators for both the temporal and spatial discretization are advocated, and facilitate a fully adaptive propagation. The framework is developed and exemplified in the context of the cl...

The paper presents a particle method framework for resolving molecular dynamics. Error estimators for both the temporal and spatial discretization are advocated and facilitate a fully adaptive propagation. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. The framework is developed and exemplified in the context of the classic...

A weak form Galerkin finite element model for the nonlinear quasi-static and fully transient analysis of initially straight viscoelastic beams is developed using the kinematic assumptions of the third-order Reddy beam theory. The formulation assumes linear viscoelastic material properties and is applicable to problems involving small strains and moderate rotations. The viscoelastic constitutive...

Abstract Three prominent low order implicit time integration schemes are the first Euler-method, second trapezoidal rule and Ellsiepen method. Its advantages stability comparatively computational cost, however, they require solution of a nonlinear system equations. This paper presents general approach for construction third Runge–Kutta methods by embedding above mentioned into class ELDIRK-meth...

In this paper, an improvement of the nearest trapezoidal approximation operator preserving the expected interval is studied, which is proposed by Grzegorzewski and Mrówka. A formula for computing the improved approximation is presented. Moreover, the nearest triangular approximation operator preserving the expected interval is also investigated. © 2007 Elsevier B.V. All rights reserved.