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Distributional solution theory for linear DAEs
Author(s) -
Trenn Stephan
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810077
Subject(s) - ode , mathematics , distribution (mathematics) , ordinary differential equation , space (punctuation) , transformation (genetics) , differential algebraic equation , multiplication (music) , algebraic number , piecewise linear function , piecewise , differential (mechanical device) , mathematical analysis , differential equation , computer science , physics , thermodynamics , chemistry , combinatorics , biochemistry , gene , operating system
A solution theory for switched linear differential–algebraic equations (DAEs) is developed. To allow for non–smooth coordinate transformation, the coefficients matrices may have distributional entries. Since also distributional solutions are considered it is necessary to define a suitable multiplication for distribution. This is achieved by restricting the space of distributions to the smaller space of piecewise–smooth distributions. Solution formulae for two special DAEs, distributional ordinary differential equations (ODEs) and pure distributional DAEs, are given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)