Work

Boundary-Value Problems of Functional Differential Equations with State-Dependent Delays

Year: 2025

Type: article

Abstract: . We prove convergence of piecewise polynomial collocation methods applied to periodic boundary value problems for functional differential equations with state-dependent delays. The state dependence of the delays leads to nonlinearities that are not locally Lipschitz continuous, preventing the direct application of general abstract discretization theoretic frameworks. We employ a weaker form of differentiability, which we call mild differentiability, to prove that a locally unique solution of the functional differential equation is approximated by the solution of the discretized problem with the expected order.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/24m1711182

Authors: Alessia Andò, Jan Sieber

Institutions: University of Udine, University of Exeter

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Udine, Gruppo Nazionale per il Calcolo Scientifico

Award: G330332393