Integro-differential polynomials and operators

Authors:
Markus Rosenkranz;Georg Regensburger
Affiliations:
Austrian Academy of Sciences, Linz, Austria;Austrian Academy of Sciences, Linz, Austria
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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Abstract

We propose two algebraic structures for treating integral operators in conjunction with derivations: The algebra of integro-differential polynomials describes nonlinear integral and differential operators together with initial values. The algebra of integro-differential operators can be used to solve boundary problems for linear ordinary differential equations. In both cases, we describe canonical/normal forms with algorithmic simplifiers.