We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and provide a theoretical estimate of the error. We conclude with some numerical experiments to further support the theoretical results.

翻译：我们将分段正交配置法推广至计算耦合更新方程与延迟微分方程的周期解。通过严格的误差分析，我们证明了相关有限元方法的收敛性，并给出了理论误差估计。最后通过数值实验进一步验证理论结果。