延迟微分方程θ-方法的稳定性分析

Stability analysis for θ -methods with delay differential equations

考虑对延迟微分方程线性θ -方法离散化后的误差分析 ,给出了新的数值方法的稳定性定义 .同时又讨论了一种Kreiss预解条件更的证明的形式 .证明了在此条件下 ,数值方法计算所得的误差随迭代矩阵的阶数线性增长 .最后 ,证明了当 1/2≤θ≤ 1时 ,线性θ

Analyses the error growth for discretizations of linear θ -methods with delay differential equations,gives a new definition of stability for the numerical method and discusses the weaker version of the Kreiss resolvent condition,under which,a stability estimate is proved to grow linearly with the order of the matrices under consideration and proves that the linear θ -method is stable if 1/2≤ θ ≤1.