Abstract. We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and Green's operators, we employ the algebra of integro-differential operators. The operations implemented for regular boundary problems include computing Green's operators as well as composing and factoring boundary problems. Our symbolic approach to singular boundary problems is new; it provides algorithms for computing compatibility conditions and generalized Green's operators.

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Introduction. We present a Maple package for computing in algebras of integro-differential operators. This provides the appropriate algebraic setting for treating boundary problems [7] for linear ordinary differential equations symbolically. They allow to formulate a boundary problem-a differential equation and boundary conditionsbut they are also expressive enough for describing its solution via an integral operator, which is called Green's operator. The implementation was tested in Maple 11, 12 and 13. It is available with an example worksheet at

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show thatprovided a factorization of the underlying differential operator-a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.