Article

Symbolic-numeric completion of differential systems by homotopy continuation

Authors:

Jan Verschelde,

Allan Wittkopf,

Wenyuan WuAuthors Info & Claims

ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation

Pages 269 - 276

https://doi.org/10.1145/1073884.1073922

Published: 24 July 2005 Publication History

Abstract

Two ideas are combined to construct a hybrid symbolic-numeric differential-elimination method for identifying and including missing constraints arising in differential systems. First we exploit the fact that a system once differentiated becomes linear in its highest derivatives. Then we apply diagonal homotopies to incrementally process new constraints, one at a time. The method is illustrated on several examples, combining symbolic differential elimination (using rifsimp) with numerical homotopy continuation (using phc).

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Cited By

Wu WReid GGolubitsky O(2009)Towards Geometric Completion of Differential Systems by PointsApproximate Commutative Algebra10.1007/978-3-211-99314-9_3(79-97)Online publication date: 21-Aug-2009
https://doi.org/10.1007/978-3-211-99314-9_3
Wu WReid GWang D(2007)Symbolic-numeric computation of implicit riquier bases for PDEProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277599(377-386)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277599
Zhou WJeffrey DReid G(2007)Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical SystemsSymbolic-Numeric Computation10.1007/978-3-7643-7984-1_20(335-347)Online publication date: 2007
https://doi.org/10.1007/978-3-7643-7984-1_20
Show More Cited By

Index Terms

Symbolic-numeric completion of differential systems by homotopy continuation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Partial differential equations

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cover image ACM Conferences

ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation

July 2005

388 pages

ISBN:1595930957

DOI:10.1145/1073884

General Chairs:
Xiao-Shan Gao
MMRC, Chinese Academy of Sciences, China
,
George Labahn
University of Waterloo, ON, Canada

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 24 July 2005

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ISSAC05: International Symposium on Symbolic and Algebraic Computation

July 24 - 27, 2005

Beijing, China

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Wu WReid GGolubitsky O(2009)Towards Geometric Completion of Differential Systems by PointsApproximate Commutative Algebra10.1007/978-3-211-99314-9_3(79-97)Online publication date: 21-Aug-2009
https://doi.org/10.1007/978-3-211-99314-9_3
Wu WReid GWang D(2007)Symbolic-numeric computation of implicit riquier bases for PDEProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277599(377-386)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277599
Zhou WJeffrey DReid G(2007)Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical SystemsSymbolic-Numeric Computation10.1007/978-3-7643-7984-1_20(335-347)Online publication date: 2007
https://doi.org/10.1007/978-3-7643-7984-1_20
Wu WReid GTrager B(2006)Application of numerical algebraic geometry and numerical linear algebra to PDEProceedings of the 2006 international symposium on Symbolic and algebraic computation10.1145/1145768.1145824(345-352)Online publication date: 9-Jul-2006
https://dl.acm.org/doi/10.1145/1145768.1145824
Leykin AVerschelde J(2006)Interfacing with the numerical homotopy algorithms in PHCpackProceedings of the Second international conference on Mathematical Software10.1007/11832225_35(354-360)Online publication date: 1-Sep-2006
https://dl.acm.org/doi/10.1007/11832225_35

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