分段常微分方程边值问题的改进COLSYS算法

Improved COLSYS algorithm for piecewise ODE BVPs

对分段定义的常微分方程边值问题的 COLSYS算法进行了改进 ,提高了其计算效率及数值稳定性 ,并且可以节省内存 ,这些优势随着分段数的增加而迅速加大。

In this paper, the algorithm of ODE solver, COLSYS, is improved to solve piecewise ODE BVPs in a more efficient way. Since the ODEs defined on different pieces are not coupled with one another, the corresponding collocation matrices containing a large number zero elements are rearranged in COLSYS subroutines to get a minimum bandwidth. Compared with those from the original method used in COLSYS, the improvement increases efficiency, accuracy and numerical stability of the solutions accordingly. The computer memory needed is also cut down greatly. The theoretical analysis and numerical experiments given in this paper show the rate of the gained speed grows in an accelerated fashion as the number of piece increases.