Piecewise orthogonal collocation for computing periodic solutions of renewal equations

TL;DR

This paper introduces a piecewise orthogonal collocation method for accurately computing periodic solutions of renewal equations, crucial in population dynamics, with proven convergence and demonstrated effectiveness through numerical experiments and bifurcation analysis.

Contribution

The paper extends orthogonal collocation techniques to renewal equations, providing rigorous convergence proofs and practical applications in bifurcation studies.

Findings

Method achieves convergence as proven theoretically.

Numerical experiments confirm theoretical accuracy.

Applications demonstrate usefulness in bifurcation analysis.

Abstract

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.