Section: New Results

Singular boundary problems

Participants : Georg Regensburger [correspondent] , Anja Korporal [RICAM, Linz] , Bruno Buchberger [RISC, Linz] , Markus Rosenkranz [Univ. Kent] .

In [55] , we present results on algorithmic methods for singular boundary problems for linear ordinary differential equations. Moreover, the implementation of integro-differential operators and the corresponding algorithms for boundary problems in the computer algebra system Maple is discussed. The operations implemented for regular boundary problems include computing Green's operators as well as composing and factoring boundary problems. For singular boundary problems, compatibility conditions and generalized Green's operators can be computed. In [94] , we give a survey and new results on our algebraic and symbolic approach to boundary problem developed over the last years. The construction of integro-differential operators and polynomials over an integro-differential algebra is described in detail along with a generic implementation of the corresponding canonical forms and algorithms.