Related papers: Lagrangian and Hamiltonian Taylor Variational Inte…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of Hamiltonian problems. In this note, we describe an…
We develop an explicit, second-order, variational time integrator for full body dynamics that preserves the momenta of the continuous dynamics, such as linear and angular momenta, and exhibits near-conservation of total energy over…
We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
This paper deals with the control of parasitism in variational integrators for degenerate Lagrangian systems by writing them as general linear methods. This enables us to calculate their parasitic growth parameters which are responsible for…
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to…
The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…
This paper is devoted to a new first order Taylor-like formula where the corresponding remainder is strongly reduced in comparison with the usual one which appears in the classical Taylor's formula. To derive this new formula, we introduce…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. In this paper…
We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical…