Premium
Second‐Order Differential Equations Exhibiting Spectral Gaps
Author(s) -
Wagner N.,
Gaul L.
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510052
Subject(s) - matrix (chemical analysis) , differential equation , sign (mathematics) , mathematics , eigenvalues and eigenvectors , function (biology) , work (physics) , sign function , order (exchange) , mathematical analysis , physics , quantum mechanics , chemistry , finance , chromatography , evolutionary biology , economics , biology
We consider the numerical solution of a linear second‐order differential equation, which is an underlying equation in many engineering applications. The response of such a system is typically dominated by a relatively small number of the lowfrequency modes. Using projections on certain eigenspaces or generalized eigenspaces of the system matrix that are induced by the matrix sign function, it is shown that the original problem may be reduced to a smaller subproblem that may be handled with significantly less computational work. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)