Factorization of linear ordinary differential operators with variable coefficients is one of the well-known methods used for solution of the corresponding differential equations. Factorization of linear partial differential operators is a much more complicated problem. An appropriate modification of the "naive" definition of factorization gives rise to a bunch of new methods of closed-form solution of a single linear partial differential equation or a system of such equations. This approach is naturally related to differential transformations---another popular method of solution of differential equations.

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure generalizes the classical theory of Laplace transformations of second-order equations in the plane.

We present an algorithm for factoring a zero-dimensional left ideal in the ring Q(x, y) [∂x, ∂y], i.e. factoring a linear homogeneous partial differential system whose coefficients belong to Q(x, y), and whose solution space is finite-dimensional over Q. The algorithm computes all the zero-dimensional left ideals containing the given ideal. It generalizes the Beke-Schlesinger algorithm for factoring linear ordinary differential operators, and uses an algorithm for finding hyperexponential solutions of such ideals.

We give a decision procedure for existence of factorixations (tlec:ompositions int.0 lower order ODEs) of nonlinear orclinary differential cquat.ionsy(") = F(z: y(x), y', .: y'"-") for the general cast (,equations with arbitrary locally nieromorphic F).The prol)lcm of factorization for the CRSC of rational F is discussed.

We discuss the problem of manipulation of expressions involving indefinite functions, integration operators and inverses of linear ordinary differential operators (LODO).Using Loewy-Ore formal theory we obtain some subnormal forms for such expressions and algorithms for verification of identities involving such expressions.

Article Free Access Share on An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator Author: S. P. Tsarev Department of Mathematics, Krasnoyarsk State Pedagogical University, Lebedevoi, 89, 660049, Krasnoyarsk, Russia Department of Mathematics, Krasnoyarsk State Pedagogical University, Lebedevoi, 89, 660049, Krasnoyarsk, RussiaView Profile Authors Info & Claims ISSAC '96: Proceedings of the 1996 international symposium on Symbolic and algebraic computationOctober 1996 Pages 226–231https://doi.org/10.1145/236869.237079Published:01 October 1996Publication History 29citation293DownloadsMetricsTotal Citations29Total Downloads293Last 12 Months34Last 6 weeks7 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF