Two ideas are combined to construct a hybrid symbolic-numeric differential-elimination method for identifying and including missing constraints arising in differential systems. First we exploit the fact that a system once differentiated becomes linear in its highest derivatives. Then we apply diagonal homotopies to incrementally process new constraints, one at a time. The method is illustrated on several examples, combining symbolic differential elimination (using rifsimp) with numerical homotopy continuation (using phc).
Categories and Subject Descriptors: G.1.8
General Terms: Algorithms, Design.
Keywords: Component of solutions, diagonal homotopy, DAE (Differential Algebraic Equation), differential elimination, hidden constraint, homotopy continuation, numerical algebraic geometry, numerical jet geometry, path following, polynomial system, witness set.
2000 Mathematics Subject Classification: Primary 34M15; Secondary 14Q99, 65H10, 68W30.
Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (ISSAC'05), July 24-27 2005, Beijing, China. Edited by Manuel Kauers, pages 269-276, ACM 2005.