A note on numerically consistent initial values for high index differential-algebraic equations

When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of w...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 34; p. 14
Main Author Arevalo, Carmen
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.12.2008
Subjects
Differential equations
Matematik
Mathematical Sciences
Natural Sciences
Naturvetenskap
Numerical analysis
Sweden
Online AccessGet full text
ISSN1068-9613
1097-4067
1097-4067

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Summary:When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the exact initial values into what we call numerically consistent initial values for the implicit Euler method. Key words. high index differential-algebraic equations, consistent initial values AMS subject classifications. 65L05
ISSN:1068-9613
1097-4067
1097-4067