A structure preserving approximation method for Hamiltonian exponential matrices

Authors:
S. Agoujil;A. H. Bentbib;A. Kanber
Affiliations:
Laboratoire LAMAI, Facultés des Sciences et Techniques Errachidia, BP 509 Boutalimine 52 000 Errachidia, Morocco;Laboratoire LAMAI, Facultés des Sciences et Techniques-Guéliz, Laboratoire de Mathématiques Appliquées et Informatique, BP 549 Marrakech, Morocco;Laboratoire LAMAI, Facultés des Sciences et Techniques-Guéliz, Laboratoire de Mathématiques Appliquées et Informatique, BP 549 Marrakech, Morocco
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

The approximation of exp(A)V where A is a real matrix and V a rectangular matrix is the key ingredient of many exponential integrators for solving systems of ordinary differential equations. In this paper we give an appropriate structure preserving approximation method to exp(A)V when A is a Hamiltonian or skew-Hamiltonian 2n-by-2n real matrix. Our approach is based on Krylov subspace methods that preserve Hamiltonian or skew-Hamiltonian structure. In this regard we use a symplectic Lanczos algorithm to compute the desired approximation.