Numerical solution of isospectral flows
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- by Mari Paz Calvo, Arieh Iserles and Antonella Zanna PDF
- Math. Comp. 66 (1997), 1461-1486 Request permission
Abstract:
In this paper we are concerned with the problem of solving numerically isospectral flows. These flows are characterized by the differential equation \[ L’ = [B(L), L], \quad L(0)=L_0, \] where $L_0$ is a $d\times d$ symmetric matrix, $B(L)$ is a skew-symmetric matrix function of $L$ and $[B,L]$ is the Lie bracket operator. We show that standard Runge–Kutta schemes fail in recovering the main qualitative feature of these flows, that is isospectrality, since they cannot recover arbitrary cubic conservation laws. This failure motivates us to introduce an alternative approach and establish a framework for generation of isospectral methods of arbitrarily high order.References
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Additional Information
- Mari Paz Calvo
- Affiliation: Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain
- Arieh Iserles
- Affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England
- Antonella Zanna
- Affiliation: Newnham College, University of Cambridge, Cambridge, England
- Received by editor(s): September 7, 1995
- © Copyright 1997 American Mathematical Society
- Journal: Math. Comp. 66 (1997), 1461-1486
- MSC (1991): Primary 65L05; Secondary 34C30
- DOI: https://doi.org/10.1090/S0025-5718-97-00902-2
- MathSciNet review: 1434938