Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems
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 thatprovided a factorization of the underlying differential operatora 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.8455
 Bibcode:
 2013arXiv1310.8455K
 Keywords:

 Computer Science  Symbolic Computation;
 Computer Science  Mathematical Software;
 Computer Science  Numerical Analysis;
 Mathematics  Classical Analysis and ODEs;
 68W30 (Primary);
 34B05;
 15A09 (Secondary)
 EPrint:
 19 pages