One step semi-explicit methods based on the Cayley transform for solving isospectral flows

✍ Scribed by F. Diele; L. Lopez; T. Politi

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 255 KB
• Volume: 89
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00236-7

✦ Synopsis

This note deals with the numerical solution of the matrix differential system

where Y0 is a real constant symmetric matrix, B maps symmetric into skew-symmetric matrices, and [B(t, Y), Y] is the Lie bracket commutator of B(t, Y) and Y, i.e. [B(t, Y), Y] = B(t, Y)Y -YB(t, Y). The unique solution of (1) is isospectral, that is the matrix Y(t) preserves the eigenvalues of Y0 and is symmetric for all t (see [1, 5]). Isospectral methods exploit the Flaschka formulation of (1) in which Y(t) is written as Y(t) = U(t)YoUT(t), for t ~> 0, where U(t) is the orthogonal solution of the differential system U' = B(t, UYoUr)U, U(O) = I, t >>, O,

(see [5]). Here a numerical procedure based on the Cayley transform is proposed and compared with known isospectral methods.