A bootstrapping approach for computing multiple solutions of differential equations

Wenrui Hao, Jonathan D. Hauenstein, Bei Hu, Andrew J. Sommese

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Discretizing systems of nonlinear algebraic differential equations yields polynomial systems. When using a fine discretization, the resulting polynomial system is often too large to solve using a direct solving approach. Our approach for solving such systems is to utilize a homotopy continuation based method arising from domain decomposition. This method solves polynomial systems arising from subdomains and then uses homotopy continuation to build solutions of the original polynomial system. We illustrate this approach on both one- and two-dimensional problems.

Original languageEnglish (US)
Pages (from-to)181-190
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume258
DOIs
StatePublished - Jan 1 2014

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Polynomial Systems
Bootstrapping
Multiple Solutions
Differential equations
Homotopy Continuation
Polynomials
Differential equation
Computing
Algebraic Differential Equations
Domain Decomposition
Nonlinear Differential Equations
Discretization
Decomposition

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Hao, Wenrui ; Hauenstein, Jonathan D. ; Hu, Bei ; Sommese, Andrew J. / A bootstrapping approach for computing multiple solutions of differential equations. In: Journal of Computational and Applied Mathematics. 2014 ; Vol. 258. pp. 181-190.
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A bootstrapping approach for computing multiple solutions of differential equations. / Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J.

In: Journal of Computational and Applied Mathematics, Vol. 258, 01.01.2014, p. 181-190.

Research output: Contribution to journalArticle

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