Symbolic-numeric completion of differential systems by homotopy continuation

Two ideas are combined to construct a hybrid symbolicnumeric 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).

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: Greg Reid, Jan Verschelde, Allan D. Wittkopf, Wenyuan Wu
• Keywords: ISSAC 2005, Numerical Homotopy Continuation, Symbolic Differential Elimination, Symbolicnumeric Differential-elimination Method