NAFeb 5, 2018
On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problemsL. Brugnano, J. I. Montijano, L. Rández
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with the numerical solution of such problems.
NAMay 22, 2019
High-order energy-conserving Line Integral Methods for charged particle dynamicsL. Brugnano, J. I. Montijano, L. Rández
In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining Hamiltonian Boundary Value Methods (HBVMs), a class of energy-conserving Runge-Kutta methods for Hamiltonian problems. A complete analysis of the new methods is provided, which is confirmed by a few numerical tests.