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Stability of time discretization, Hurwitz determinants and order stars

by R. Jeltsch

(Report number 1995-12)

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.

Keywords: stability of time discretizations, ordinary differential equations, partial differential equations, Von Neumann analysis, Routh algorithm, fraction free, order stars

@Techreport{J95_179,
  author = {R. Jeltsch},
  title = {Stability of time discretization, Hurwitz determinants and order stars},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-12.pdf },
  year = {1995}
}

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