A Hybrid Numerical Technique for the Solution of a Class of Implicit Matrix Differential Equation

Buono, Nicoletta Del; Lopez, L.

doi:10.1007/978-3-540-25944-2_60

Cited by 1 publication

(2 citation statements)

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“…Despite the simplicity of the substituting approach, where no explicit inversion of matrices is required, the above system has a double dimension with respect to the original one. Moreover, when one has to deal with differential equations whose solution Y (t) possesses an additional structure, as in case of ODEs evolving on the oblique manifold, the substituting approach does not preserve such a structure [13][14][15][16].…”

Section: Problems On the General Linear Groupmentioning

confidence: 97%

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Numerical methods for ordinary differential equations on matrix manifolds

Lopez

2007

Journal of Computational and Applied Mathematics

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In recent years differential systems whose solutions evolve on manifolds of matrices have acquired a certain relevance in numerical analysis. A classical example of such a differential system is the well-known Toda flow. This paper is a partial survey of numerical methods recently proposed for approximating the solutions of ordinary differential systems evolving on matrix manifolds. In particular, some results recently obtained by the author jointly with his co-workers will be presented. We will discuss numerical techniques for isospectral and isodynamical flows where the eigenvalues of the solutions are preserved during the evolution and numerical methods for ODEs on the orthogonal group or evolving on a more general quadratic group, like the symplectic or Lorentz group. We mention some results for systems evolving on the Stiefel manifold and also review results for the numerical solution of ODEs evolving on the general linear group of matrices.

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Section: Problems On the General Linear Groupmentioning

confidence: 97%

“…Particularly, by considering the v-stage explicit RK method identified by the Butcher array (15) with c = (c 1 , . .…”

Section: Theorem 1 Let Y (T) Be the Solution Ofmentioning

confidence: 99%