常微分方程初值问题的完全三阶并行块算法及实验阶研究

RESEARCH ON THE RECURRENCE FORMULAS OF THE WHOLE THREE ORDER NUMERICAL METHODS AND THE EXPERIMENT ORDER FOR INITIAL VALUE PROBLEM OF ORDINARY DIFFERENTIAL EQUATIONS

针对常微分方程初值问题中一些不完全组合方法达不到高阶校正公式计算结果的现象,本文提出并推导了一个完全三阶并行块方法,证明了它的相容性、稳定性和收敛性.最后,在对实验数据进行分析的基础上,提出实验阶概念;并通过实验数据对比,证明本文提出的方法达到完全三阶.

According to some composition formulas for the initial value problem of ordinary differ- ential equations cannot got the results of the highest order of the correction equation, this paper presented a kind of new methods of the three order recurrence and gave the process for their derivation. Then, their correlation, stability and convergence were proved. And finally, on the bases of the test data, the experiment order was presented. Through the contrast of the test data, the new methods presented in the paper were proved a kind of whole three order formulas..