Problems involving rolling without slipping or no sideways skidding, to name a few, introduce velocity-dependent constraints that can be efficiently treated by the method of Lagrange multipliers in Lagrangian formulation classical equations motion. In doing so one finds, as bonus, constraint forces, which must independent solution motion, and only depend on generalized coordinates velocities, w...

The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

In this paper we study the dynamic behavior of an isotropic KirchhoffLove beam and investigate the equilibrium position of an Euler-Bernoulli beam. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, we simulate the behavior by means of variational integrators and, in particular, AVIs (Asynchronous Variational Integrators). We place special emphasis on the geometric structure ...

The singular function boundary integral method is applied for the solution of a Laplace equation problem over an L-shaped domain. The solution is approximated by the leading terms of the local asymptotic solution expansion, while the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. Estimates of great accuracy are obtained for the leading singular coe:cients, a...

The variational free-Lagrange (VFL) method for shallow water is a free-Lagrange method with the additional property that it preserves the variational structure of shallow water. The VFL method was first derived in this context by Augenbaum (1984) who discretised Hamilton’s action principle with a free-Lagrange data structure. The primary purpose of this article is to demonstrate, through the us...

We analyze a second order pure Lagrange-Galerkin method for variable coefficient convection-(possibly degenerate) diffusion equations with mixed Dirichlet-Robin boundary conditions. In a previous paper the proposed second order pure Lagrangian time discretization scheme has been introduced and analyzed for the same problem. Moreover, the l(H) stability and l(H) error estimates of order O(∆t) ha...

The Lagrange multiplier based rate−distortion optimization has been proved an effective technique in hybrid video codec design. To improve the coding efficiency, an efficient Lagrange multiplier selection method is presented in this paper. As an extension to our previous work, the Laplace distribution based rate model is further refined by taking correlations among successive frames into accoun...

It is demonstrated that the pre-dual for problems with total bounded variation regularization terms can be expressed as bilaterally constrained optimization problem. Existence of a Lagrange multiplier and an optimality system are established. This allows to utilize efficient optimization methods developed for problems with box constraints in the context of bounded variation formulations. Here, ...