A Maple program for factorization of LPDOs in two variables

Abstract:
Historically, so-called "naive"' factorization of LPDO is considered as unproductive. Miller was the first to obtain results for LPDO of order 2 and 3. Last year Grigoriev and Schwarz modified the idea for an arbitrary order of LPDO.

It turned out, that for this general case it is possible also to follow Millner's idea directly, i.e. to extract first-order factor of LPDO on the left and therefore reduce its order on each step of an algorithm. Coefficients of factors and conditions of its extracting were written out explicitly for any order of LPDO. The first version of the MAPLE-implementation provides us, for example, with some new factorizations for well-known Landau operator. The paper includes some ideas of application to numerical simulations.