arXiv subjects

Alessia Ando'

Publications and source records attributed to Alessia Ando'.

2 recordsLinked to original sources

arXiv2024

Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework

Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be recast as abstract differential equations, which motivates the present work. The result is a general approach that allows us to define the methods explicitly and analyze their convergence properties in a unifying way.

math.NA↗

arXiv2023

Piecewise orthogonal collocation for computing periodic solutions of renewal equations

We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally, we show some numerical experiments confirming the theoretical results, and a couple of applications in view of bifurcation analysis.

math.NA↗