强稳定的最优单步法公式

Optimal Formulae of Strongly StaBle Single-step Algorithm

本文研究一阶常微分方程灵敏值解的收敛性与稳定性 ,利用最优化方法 ,确定最优系数 ,导出两个强稳定的单步公式 ,并加以优化和改进 ,得到新的算法。经过实际计算 ,结果优目前的单步公式。同时也验证了梯形公式。

The convergence properth and stability of numerical solution in first order differential equation are studied in this paper.The optimal coefficeents are determined by optimal method and two strongly stable formulas in single-step method are got.optimized and improved.Then a new algorithmis formed.The practical calculation shows that the results are better than that of the present formulas in single-step method.And trapezoidal formula is verfied.