A bootstrapping approach for computing multiple solutions of differential equations

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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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 - 2014

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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