Kurt Schlacher, Andreas Kugi,
"Symbolic Methods for Systems of Implicit Ordinary Differential Equations"
, in Mechanics of Structures and Machines, Vol. 30, Nummer 3, Seite(n) 411-429, 8-2002, ISBN: 0890-5452
Original Titel:
Symbolic Methods for Systems of Implicit Ordinary Differential Equations
Sprache des Titels:
Englisch
Original Kurzfassung:
This contribution deals with the equivalence problems for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of some normal form, and vice versa. The system is identified with the submanifold in a suitable jet-space, defined by the equations. Therefore, a short introduction to jet-theory is presented, as well as its application to systems of differential equations. We present several results for well-determined and under-determinded systems and give formulas that describe the transform to an appropriate normal form. Apart from the theoretical results, we give several sketches of computer algebra-based algroithms necessary to solve these problems efficiently.
Sprache der Kurzfassung:
Estnisch
Englischer Titel:
Symbolic Methods for Systems of Implicit Ordinary Differential Equations
Englische Kurzfassung:
This contribution deals with the equivalence problems for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of some normal form, and vice versa. The system is identified with the submanifold in a suitable jet-space, defined by the equations. Therefore, a short introduction to jet-theory is presented, as well as its application to systems of differential equations. We present several results for well-determined and under-determinded systems and give formulas that describe the transform to an appropriate normal form. Apart from the theoretical results, we give several sketches of computer algebra-based algroithms necessary to solve these problems efficiently.
Forschungs-