Banach空间中非线性刚性DDEs θ-方法渐近稳定性

Asymptotic Stability of θ-methods for Nonlinear Stiff Delay Differential Equations in Banach Spaces

科学与工程技术中存在大量刚性问题,尽管问题本身是整体良态的,但当使用内积范数时,其最小单边 Lipschitz 常数却不可避免地取非常巨大的正值,导致基于此常数下建立的数值稳定性理论失效。针对求解 Banach 空间中一类非线性刚性延迟微分方程初值问题的线性和单支θ -方法建立了渐近稳定的充分条件,即使按内积范数其单边 Lipschitz 常数十分巨大的问题仍有可能属于这类问题,因而所建立的结果对于这些问题同样是适用的。

The sufficient conditions are established for the linear and one-lag θ-methods to be asymptotic stable when applied to a class of nonlinear Stiff delay differential equations in Banach spaces. For some stiff problems in the fields of scientific and engineering, it may happen that the one-sided Lipschitz constant is very large even if the problem is well conditioned, which causes the existing numerical theory in Hilbert space impracticable, but the stability criteria established in the present research are still applicable.