Symbolic Methods for the Equivalence Problem of Systems of Implicit Ordinary Differential Equations
Sprache des Vortragstitels:
Englisch
Original Tagungtitel:
Conference Symbolic and Numeric Computation SNSC’01
Sprache des Tagungstitel:
Englisch
Original Kurzfassung:
This contribution deals with the equivalence problem for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of a given normal form and vice versa. Since we describe this system as a submanifold in a suitable jet-space, we present some basics from differential and algebraic geometry and give a short introduction to jet-theory and its application to systems of differential equations. The main results of this contribution are two solutions for the equivalence problem where time derivatives of the input are admitted or not. Apart from the theoretical results we give a sketch for computer algebra based algroithms necessary to solve these problems efficiently.
Sprache der Kurzfassung:
Englisch
Englischer Vortragstitel:
Symbolic Methods for the Equivalence Problem of Systems of Implicit Ordinary Differential Equations
Englischer Tagungstitel:
Conference Symbolic and Numeric Computation SNSC’01
Englische Kurzfassung:
This contribution deals with the equivalence problem for systems of implicit ordinary differential equations. Equivalence means that every solution of the original set of equations is a solution of a given normal form and vice versa. Since we describe this system as a submanifold in a suitable jet-space, we present some basics from differential and algebraic geometry and give a short introduction to jet-theory and its application to systems of differential equations. The main results of this contribution are two solutions for the equivalence problem where time derivatives of the input are admitted or not. Apart from the theoretical results we give a sketch for computer algebra based algroithms necessary to solve these problems efficiently.