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On the spectrum of families of matrices with applications to stability problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1386)

Abstract

The stability properties of numerical methods for hyperbolic and parabolic PDE are studied by using the method of lines. The notion of spectrum of a family of matrices permits the use of the usual concept of A-stability for ODEs. The problem related to the consistency is analyzed as well as the connection with the Von-Neumann stability test.

Work performed within the activities of the "Centro Nazionale di Matematica Computazionale" supported by the "Ministero della Pubblica Istruzione".

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© 1989 Springer-Verlag

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Di Lena, G., Trigiante, D. (1989). On the spectrum of families of matrices with applications to stability problems. In: Bellen, A., Gear, C.W., Russo, E. (eds) Numerical Methods for Ordinary Differential Equations. Lecture Notes in Mathematics, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089230

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  • DOI: https://doi.org/10.1007/BFb0089230

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51478-7

  • Online ISBN: 978-3-540-48144-7

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