Convergence analysis of waveform relaxation for nonlinear differential-algebraic equations of index one

We give a new and simple convergence theorem on the waveform relaxation (WR) solution for a system of nonlinear differential-algebraic equations of index one. We show that if the norms of certain matrices derived from the Jacobians of the system functions are less than one, then the WR solution converges. The new sufficient condition includes previously reported conditions as special cases. Examples are given to confirm the theoretical analysis.