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arXiv · 2410.07375

Boundary-value problems of functional differential equations with state-dependent delays

Alessia andò·Jan Sieber
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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.

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Alessia andò, Jan Sieber. 2024-10-09. Boundary-value problems of functional differential equations with state-dependent delays. https://arxiv.org/abs/2410.07375

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