刚性延迟微分方程数值仿真的两步连续Rosenbrock方法

Two-Step Continuity Rosenbrock Methods of Numerical Simulation for Stiff Delay Differential Equations

在科学、工程领域的研究和应用中,常常会遇到刚性延迟微分方程系统,对它们进行数值仿真时,通常需要稳定性较好计算复杂性小的方法。为了数值仿真刚性延迟微分方程系统,构造了一类用于求解刚性延迟微分方程的两步连续Rosenbrock方法,讨论了方法的构造,方法的阶条件,证明了方法的收敛性,分析了方法的稳定性。这种方法具有GP-稳定性,数值试验表明方法是有效的。

In the area of research and application of science and engineering, stiff delay differential equations are often met. For numerical simulating stiff delay differential equations, numerical methods of good numerical stability and easy implementation are needed. For simulating the stiff delay differential equations, a class of two-step continuity Rosenbrock methods were proposed. The construction, order conditions, numerical stability and convergence of the methods were studied. The methods constructed are GP-stable and the numerical experiments show that the methods are efficient.