Symbolic-numeric completion of differential systems by homotopy continuation

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).