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The ☆ -product approach for linear ODEs: A numerical study of the scalar case

Pozza, Stefano, Van Buggenhout, Niel (2023)

Programs and Algorithms of Numerical Mathematics

Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...

The relationship between the infinite eigenvalue assignment for singular systems and the solvability of polynomial matrix equations

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.

The Second Half-With a Quarter of a Century Delay

O. Diekmann, M. Gyllenberg (2008)

Mathematical Modelling of Natural Phenomena

We show how results by Diekmann et al. (2007) on the qualitative behaviour of solutions of delay equations apply directly to a resource-consumer model with age-structured consumer population.

Currently displaying 241 – 260 of 475