带Neumann边界条件的延迟泛函偏微分方程线性θ-方法的稳定性

Stability of Linear θ-Method for Delay Partial Functional Differential Equations with Neumann Boundary Conditions

本文主要研究延迟泛函偏微分方程Neumann边值问题的数值稳定性.首先,获得解析解渐近稳定的充分条件,接着用线性θ-方法离散方程,对于参数θ的不同取值范围,讨论数值解的稳定性,与相应的Dirichlet边值问题相比,本文的结论更直观且易于验证.最后,给出了一些用以检验理论结果的数值例子.

This paper is mainly concerned with the numerical stability of delay partial functional differential equations with Neumann boundary conditions. Firstly, the sufficient condition of asymptotic stability of analytic solutions is obtained. Secondly, the linearθ-method is applied to discretize the above mentioned equation, and the stability of the numerical solutions is discussed for different ranges of parameter θ. Compared with the corresponding equation with Dirichlet boundary conditions, our results are more intuitive and easier to verify. Finally, some numerical examples are presented to illustrate our theoretical results.