Abstract
We shall review stability requirements for time discretizations of ordinary and partial differential equations. If a constant time step is used and the method involves more than two time levels stability is always related to the location of roots of a polynomial in circular or half plane regions. In several cases the coefficients of the polynomial depend on a real or complex parameter. Hurwitz determinants allow to create a fraction free Routh array to test the stability of time discretizations. A completely different technique, called order stars, is used to relate accuracy of the schemes with their stability.
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© 1996 Birkhäuser Verlag Basel
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Jeltsch, R. (1996). Stability of Time Discretization, Hurwitz Determinants and Order Stars. In: Jeltsch, R., Mansour, M. (eds) Stability Theory. ISNM International Series of Numerical Mathematics, vol 121. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9208-7_20
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DOI: https://doi.org/10.1007/978-3-0348-9208-7_20
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