θ型波形松弛方法A稳定的新条件

New Conditions of A-stability for θ Type of Waveform Relaxation Methods

波形松弛(WR)方法是求解高维弱耦合微分方程组的有效方法,由于很多实际问题的模型是刚性微分方程,这需要所使用的WR方法有很好的稳定性,而A稳定正是这样的性质.关于WR方法A稳定性的研究很少,最近我们研究了θ型WR方法的A稳定,给出了几个充分条件,但其对WR方法A稳定和分裂方式的关系的描述不够清晰.本文给出了A稳定的新条件,这些条件描述了表示分裂方式的角度所满足的条件,更好地阐明了WR方法的分裂方式对其A稳定的影响方式.

The waveform relaxation(WR)method can solve effectively the weakly coupled differential equations with very high dimensions.It is necessary to use the WR methods with very good property of stability because many models used in application are stiff differential equations.A-stability is exactly such property.There exist very few works on A-stability of WR methods.Recently,we have studied A-stability of type θ of WR methods,obtained some sufficient conditions of A-stability,but fail to find the obvious relation between A-stability and splitting way of WR methods.Some new conditions of A-stability are given in this paper,these conditions describe what need to be satisfied for the angle of representing the splitting way,which explore how splitting way of WR methods affect its A-stability.