arXiv subjects

Bogusław Ratkiewicz

Publications and source records attributed to Bogusław Ratkiewicz.

2 recordsLinked to original sources

arXiv2010

Energy-preserving numerical schemes of high accuracy for one-dimensional Hamiltonian systems

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete gradient schemes and integrators of arbitrary high order. In numerical experiments we compare our integrators with some other numerical schemes, including the standard discrete gradient method, the leap-frog scheme and a symplectic scheme of 4th order. We study the error accumulation for very long time and the conservation of the energy integral.

math.NA↗

arXiv2010

Discrete gradient algorithms of high order for one-dimensional systems

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories in the phase space. The accuracy of our integrators is higher by several orders of magnitude as compared with the standard discrete gradient scheme (modified midpoint rule) and, what is more, our schemes have very high accuracy even for large time steps.

physics.comp-ph↗