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.
Original language  English 

Publication date  2010 

Publication status  Published  2010 

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@misc{891dc99f4f0a47b68984ac19c15e5cfe,
title = "A generalized Allwright formula and the vector Riccati equation",
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.",
author = "Andersen, {Kurt Munk} and Allan Sandqvist",
year = "2010",
language = "English",
type = "Other",
}
TY  ICOMM
T1  A generalized Allwright formula and the vector Riccati equation
AU  Andersen, Kurt Munk
AU  Sandqvist, Allan
PY  2010
Y1  2010
N2  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.
AB  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.
M3  Net publication  Internet publication
ER 