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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