Control-based Approach to Numerical Integration of Rolling Equations

Numerical integration of variational equations.

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing ...

A new approach to the numerical solution of system of dual fuzzy polynomial equations

Geometric Numerical Integration of Differential Equations

Geometric Numerical Integration of Differential Equations

What is geometric integration? ‘Geometric integration’ is the term used to describe numerical methods for computing the solution of differential equations, while preserving one or more physical/mathematical properties of the system exactly (i.e. up to round–off error)1. What properties can be preserved in this way? A first aspect of a dynamical system that is important to preserve is its phase ...

Numerical Integration of Damped Maxwell Equations

We study the numerical time integration of Maxwell’s equations from electromagnetism. Following the method of lines approach we start from a general semidiscrete Maxwell system for which a number of time-integration methods are considered. These methods have in common an explicit treatment of the curl terms. Central in our investigation is the question how to efficiently raise the temporal conv...