The Explicit Computation of Integration Algorithms and First Integrals for Ordinary Differential Equations with Polynomial Coefficients Using Trees

@inproceedings{Crouch1992TheEC,
  title={The Explicit Computation of Integration Algorithms and First Integrals for Ordinary Differential Equations with Polynomial Coefficients Using Trees},
  author={Peter E. Crouch and Robert L. Grossman},
  booktitle={ISSAC},
  year={1992}
}
This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k[x1, . . ., xN ], where k = R or C, F denotes a differential operator with coefficients from R, and g ∈ R, we describe data… CONTINUE READING