Symbolic-Numeric Completion of Differential Systems by Homotopy Continuation

G. Reid, J. Verschelde, A. Wittkopf, W. Wu


We are concerned with identifying and including missing constraints arising in differential systems. Two ideas are combined into a new hybrid symbolic-numeric differential-elimination method. First we exploit that a system once differentiated becomes linear in its highest derivatives. Then we apply diagonal homotopies to incrementally process the newly found constraints. The new method is illustrated on several examples, combining symbolic differential elimination (using rifsimp) and numerical homotopy continuation (using phc).