A generalized Allwright formula and the vector Riccati equation
Classical Analysis and ODEs
2010-10-28 v1
Abstract
A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation, and in a similar way the generalized formula is connected with a special type of a differential system called a vector Riccati equation. Moreover,the classical result that a scalar differential equation is a Riccati equation if and only if its general solution is a fractional linear function of the starting value, is also generalized to a differential system.
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Cite
@article{arxiv.1010.5702,
title = {A generalized Allwright formula and the vector Riccati equation},
author = {Kurt Munk Andersen and Allan Sandqvist},
journal= {arXiv preprint arXiv:1010.5702},
year = {2010}
}
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23 pages