An Automated Confluence Proof for an Infinite Rewrite System Parametrized over an Integro-Differential Algebra

Abstract

In our symbolic approach to boundary problems for linear ordinary differential equations we use the algebra of integro-differential operators as an algebraic analogue of differential, integral and boundary operators (Section 2). They allow to express the problem statement (differential equation and boundary conditions) as well as the solution operator (an integral operator called “Green’s operator”), and they are the basis for operations on boundary problems like solving and factoring [14,17]. A survey of the implementation is given in [18].