常微分方程波形松弛方法的收敛稳定

波形松弛方法是一种用于近似求解常微分方程的迭代方法，实际计算时，初始值和每次迭代计算不可避免存在误差， 因此有必要研究误差的传播规律， 即稳定性。对常微分方程， 证明了在Lipschitz 条件下WR 方法是收敛稳定的，即在标准收敛条件下，只要初值和历次迭代的误差足够小，由WR 方法所得近似解的扰动能被控制在给定范围内。

Convergent stability of waveform relaxation methods for ordinary differential equations

The waveform relaxation (WR) method is an iterative method for the approximate solution of ordinary differential equations (ODEs). In actual calculation, the initial value and iterative calculation inevitably have errors. Thus, it is necessary to study the propagation law of errors, i.e., the stability. The convergent stability of WR methods for ODEs is proved under the Lipschitz condition. That is, under standard convergence conditions, the perturbation of approximate solutions obtained by WR methods can be controlled within a given range as long as the error between the initial value and the previous iteration is small enough.