Symbolic-numeric completion of differential systems by homotopy continuation

Authors:
Greg Reid;Jan Verschelde;Allan Wittkopf;Wenyuan Wu
Affiliations:
University of Western Ontario, London, ON, Canada;University of Illinois at Chicago, Chicago, IL;Simon Fraser University, Burnaby, British Columbia, Canada;University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

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).