中文摘要：

本文探讨非线性指标-3微分-代数系统的波形松弛算法所涉及的理论模型和具体算例的求解。对于收敛性问题，我们利用谱半径条件证明该理论模型的收敛性，所得结论的收敛性条件相对较弱，并利用算例测试了收敛定理的正确性。结果显示：在求解非线性微分-代数系统时，波形松弛类算法是具有内在并行性的有效算法。

英文摘要：

This paper discusses theoretical models and numerical experiments of waveform relaxation methods for solving nonlinear differential-algebraic systems of index-3. To investigate the convergence problem, we study the convergence performance of iteration models by using the spectra property. The derived convergence conditions are relatively weaker than existing ones. Numerical experiment has tested the theoretical models. In particular, the waveform relaxation methods are efficient algorithms which possess immanent parallel for solving the non-linear differential-algebraic, system.