适定且收敛的全部线性二步公式的推导和分析

Deduction and Analysis of All Well Posed Convergence Linear 2-steps Methods Formula

应用MATLAB的符号运算,推导了常微分方程初值问题适定的线性二步法全部公式,并利用关于线性方程组多步法公式的收敛条件,筛选出其中收敛的公式,计算出了公式的分数形式的系数,误差主项系数,阶数,绝对稳定区间。运用根轨迹法绘制了其中绝对稳定的公式的稳定区域的图形,并对以上公式的性能作出了简单分析,特别是推导和证明了一个新的二步二阶A-稳定公式。

By means of symbol operation of Matlab and the convergent condition of the linear muhistp method formula, the authors attained the well posed convergent formulas directly for all linear 2-step methods. Some convergent formulas are gotten after screening and the fraction coefficients, errors coefficients, orders and intervals of absolute stability are calculated. Then figure of region of absolute stability of the absolute stability formula is drawn by means of root locus method. The performance of those formulas simply is analyzed. One new A - stable formula of linear 2-step methods of order 2 is derived and proved.