A bootstrapping approach for computing multiple solutions of differential equations
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- 作者：Wenrui Hao ; Jonathan D. Hauenstein ; Bei Hu ; Andrew J. Sommese
- 关键词：65N55 ; 65M22 ; 65H10 ; 65L10
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2014
- 出版时间：1 March, 2014
- 年：2014
- 卷：258
- 期：Complete
- 页码：181-190
- 全文大小：824 K
文摘
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.