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Positivity inheritance for linear problems
Author(s) -
Baum A.K.,
Mehrmann Volker
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010291
Subject(s) - ode , mathematics , ordinary differential equation , matrix (chemical analysis) , monotonic function , runge–kutta methods , differential equation , linear multistep method , differential algebraic equation , mathematical analysis , chemistry , chromatography
We discuss the numerical solution of positive Differential‐Algebraic‐Equations (DAEs). For Ordinary Differential Equations (ODEs) where the system matrix is a ‐M‐Matrix, Runge‐Kutta‐ or Multistep‐Method are positive if the stepsize is chosen within the absolutely monotonicity radius of the considered method. We extend this concept to matrix pairs and present conditions for positivity preserving discretizations of linear, time‐invariant DAEs. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)