Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Geometric completion of differential systems using numeric-symbolic continuation
ACM SIGSAM Bulletin
Homotopies for Intersecting Solution Components of Polynomial Systems
SIAM Journal on Numerical Analysis
Symbolic-numeric completion of differential systems by homotopy continuation
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Notes on triangular sets and triangulation-decomposition algorithms II: differential systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Symbolic-numeric computation of implicit riquier bases for PDE
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
The computational difficulty of completing nonlinear pde to involutive form by differential elimination algorithms is a significant obstacle in applications. We apply numerical methods to this problem which, unlike existing symbolic methods for exact systems, can be applied to approximate systems arising in applications.We use Numerical Algebraic Geometry to process the lower order leading nonlinear parts of such pde systems. The irreducible components of such systems are represented by certain generic points lying on each component and are computed by numerically following paths from exactly given points on components of a related system. To check the conditions for involutivity Numerical Linear Algebra techniques are applied to constant matrices which are the leading linear parts of such systems evaluated at the generic points. Representations for the constraints result from applying a method based on Polynomial Matrix Theory.Examples to illustrate the new approach are given. The scope of the method, which applies to complexified problems, is discussed. Approximate ideal and differential ideal membership testing are also discussed.