Numerical methods for Hermitian unitary differential systems
type: Item
instance of: scholarly article
title: Numerical methods for Hermitian unitary differential systems
zbMATH Open document ID: 0941.65065
DOI: 10.1016/S0377-0427(99)00137-5
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-20T00:00:00Z
review text: The paper deals with the numerical integration of unitary differential systems of the form \[ Y'(t)=A(t,Y(t))Y(t), \quad Y(t_0)=Y_0, \quad t\geq t_0, \tag{1} \] where \(Y_0\) is a unitary matrix and \(A(t,Y)\) is skew-Hermitian. The purpose of this paper is to study unitary differential systems whose solutions are also Hermitian for all \(t\) and unitary numerical integrators which are also Hermitian integrators. It is known that in the case when the unitary solution of (1) is also Hermitian for all \(t,\) the known unitary schemes are not generally Hermitian-preserving integrators. The authors examine the known unitary-preserving methods (the \(s\)-stage Gauss-Legendre-Runge-Kutta schemes, projected methods, the Cayley methods, and isospectral methods) to determine whether they are also Hermitian-preserving integrators. It is proved that this is the case for the Cayley unitary-preserving methods. The authors also show how isospectral methods can be used to obtain Hermitian-preserving integrators. The results of numerical tests are provided for some linear and nonlinear problems of Hermitian unitary type for the comparison of different unitary integrators.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1398824
zbMATH Keywords: unitary differential system
zbMATH Keywords: Hermitian numerical integrator
zbMATH Keywords: numerical examples
zbMATH Keywords: unitary-preserving methods
zbMATH Keywords: \(s\)-stage Gauss-Legendre-Runge-Kutta schemes
zbMATH Keywords: projected methods
zbMATH Keywords: Cayley methods
zbMATH Keywords: isospectral methods
author: Nicoletta Del Buono
author: Luciano Lopez
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1398824