A bootstrapping approach for computing multiple solutions of differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:258

Article

Hao, Wenrui³  Hauenstein, Jonathan D.²  Hu, Bei¹  Sommese, Andrew J.¹ 

[1] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[3] Ohio State Univ, Math Biosci Inst, Columbus, OH 43210 USA

关键词: Domain decomposition;    Homotopy continuation;    Differential equations;    Multiple solutions;    Numerical algebraic geometry;   

DOI  :  10.1016/j.cam.2013.09.007

来源: Elsevier

【 摘 要 】

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. Published by Elsevier B.V.

【 授权许可】

Free