Regular and Singular Boundary Problems in Maple

TL;DR

This paper introduces a Maple package for solving linear ordinary differential boundary problems, including regular and singular types, using algebraic and symbolic methods for operators and boundary conditions.

Contribution

It presents a novel symbolic approach for singular boundary problems, enabling computation of compatibility conditions and generalized Green's operators.

Findings

Implemented algorithms for regular boundary problems

Developed methods for singular boundary problems

Enhanced symbolic computation capabilities in Maple

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.