比例延迟微分方程组Rosenbrock方法的渐近稳定性

Asymptotic Stability of Rosenbrock Methods for System of Pantograph Equation

讨论用一类变步长Rosenbrock方法求解线性比例延迟微分方程组的渐近稳定性,证明了在无穷远点严格稳定的变步长Rosenbrock方法能够保持原线性系统的渐近稳定性。数值试验进一步验证了算法的理论分析的正确性。

The asymptotic stability of Rosenbrock methods with variable stepsize for the linear system of pantograph equation was discussed, and it is shown that strictly stable at infinity Rosenbrock method with variable stepsize can preserve the asymptotic stability of underlying linear system. Numerical experiment further confirms the theoretical results of numerical analysis.