Composing and Factoring Generalized Green’s Operators and Ordinary Boundary Problems

  • Anja Korporal
  • Georg Regensburger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8372)

Abstract

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 that—provided 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.

Keywords

Linear boundary problem singular boundary problem generalized Green’s operator reverse order law integro-differential operator factorization ordinary differential equation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Anja Korporal
    • 1
  • Georg Regensburger
    • 1
  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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