We consider nonlinear stability and conservation properties of ODEs with a unifying approach. We show that our theory can be applied to dynamical systems in both the continuous and the discrete case. For this reason, we introduce the concept of pxp sesquilinear forms and pxp-inner products on finite dimensional vector spaces. In particular, we study two classes of functions related to the operators dealing with dissipative, unitary and symplectic ODEs. With this approach, the well-known conditions for BN-stable, unitary and symplectic Runge-Kutta methods are proved in a unifying way.
A unifying approach to stability and invariance properties of ODEs
RAGNI, Stefania;
1998
Abstract
We consider nonlinear stability and conservation properties of ODEs with a unifying approach. We show that our theory can be applied to dynamical systems in both the continuous and the discrete case. For this reason, we introduce the concept of pxp sesquilinear forms and pxp-inner products on finite dimensional vector spaces. In particular, we study two classes of functions related to the operators dealing with dissipative, unitary and symplectic ODEs. With this approach, the well-known conditions for BN-stable, unitary and symplectic Runge-Kutta methods are proved in a unifying way.File in questo prodotto:
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