Related papers: Geometric numerical integrators for Hunter-Saxton-…

In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…

Many Hamiltonian problems in the Solar System are separable or separate into two analytically solvable parts, and thus give a great chance to the development and application of explicit symplectic integrators based on operator splitting and…

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a…

Some explicit algorithms for higher order symplectic integration of a large class of Hamilton's equations have recently been discussed by Mushtaq \emph{et. al}. Here we present a Python program for automatic numerical implementation of…

In this paper we investigate the application of pseudo-transient-continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations. We will outline a residual…

We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann type boundary condition. We adopt the hybridizable discontinuous Galerkin method…

This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…

We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem…

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…

This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying a algebro-geometric initial value problem. Our main tools…

In this article, we treat G_2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G_2-structure; in…

We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular…

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…

Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using…

We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and…

We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures,…