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Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients

Authors:

Nedialko S. Nedialkov,

John D. PryceAuthors Info & Claims

Volume 45, Issue 3

Pages 561 - 591

https://doi.org/10.1007/s10543-005-0019-y

Published: 01 September 2005 Publication History

Abstract

This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT, 41 (2001), pp. 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and contain derivatives of order higher than one. Algorithmic details are given.

Second, it proves that either the method succeeds in the sense of computing TCs of the local solution, or one of a number of detectable error conditions occurs.

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Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients

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Published In

cover image BIT

BIT Volume 45, Issue 3

Sep 2005

220 pages

ISSN:0006-3835

Issue’s Table of Contents

Copyright © 2005 Springer-Verlag.

Publisher

BIT Computer Science and Numerical Mathematics

United States

Publication History

Published: 01 September 2005

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Cited By

Stocco DBertolazzi E(2024)Symbolic matrix factorization for differential-algebraic equations index reductionJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115898448:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.cam.2024.115898
Corless R(2024)An Hermite–Obreshkov method for 2nd-order linear initial-value problems for ODENumerical Algorithms10.1007/s11075-023-01738-z96:3(1109-1141)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/s11075-023-01738-z
Boulier FLemaire F(2024)On Formal Power Series Solutions of Regular Differential ChainsComputer Algebra in Scientific Computing10.1007/978-3-031-69070-9_6(82-99)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-69070-9_6
Eriksson OPalmkvist VBroman DDe Roover CRumpe BShaikhha A(2023)Partial Evaluation of Automatic Differentiation for Differential-Algebraic Equations SolversProceedings of the 22nd ACM SIGPLAN International Conference on Generative Programming: Concepts and Experiences10.1145/3624007.3624054(57-71)Online publication date: 22-Oct-2023
https://dl.acm.org/doi/10.1145/3624007.3624054
Corless R(2023)Blendstrings: an environment for computing with smooth functionsProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597117(199-207)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597117
Zolfaghari RNedialkov N(2023)An Hermite-Obreschkoff method for stiff high-index DAEBIT10.1007/s10543-023-00955-163:1Online publication date: 18-Feb-2023
https://dl.acm.org/doi/10.1007/s10543-023-00955-1
Tan GNedialkov NPryce J(2022)Conversion methods for improving structural analysis of differential-algebraic equation systemsBIT10.1007/s10543-017-0655-z57:3(845-865)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10543-017-0655-z
McKenzie RPryce J(2022)Structural analysis based dummy derivative selection for differential algebraic equationsBIT10.1007/s10543-016-0642-957:2(433-462)Online publication date: 11-Mar-2022
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Scholz LSteinbrecher A(2022)Regularization of DAEs based on the Signature methodBIT10.1007/s10543-015-0565-x56:1(319-340)Online publication date: 11-Mar-2022
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Nedialkov NPryce J(2022)Solving differential-algebraic equations by Taylor series (II): Computing the System Jacobian BIT10.1007/s10543-006-0106-847:1(121-135)Online publication date: 11-Mar-2022
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