菲波纳奇数列在常微分方程外推方法中的应用

Fibonacci Sequence fOR Ordinary Differential Equation Extrapolation Methods

§1.引言 Deuflhard在关于常微分方程外推方法的综合报告[1]中认为“在早期的论文中,外推表依可用于无限排列(按两个下标)的想法加以分析:在数列?

In a survey on ordinary differential equation extrapolation methods, Deuflhard indicatedthat 'the Toeplitz condition is no longer needed'. Numerical stability is however an inevitableproblem, so long as the extrapolation is performed on a computer with finite digits. To ensure thenumerical stability, the Toeplitz condition should not be neglected. Especially, the harmonicsequence used by Deuflhard in the extrapolation procedure does not hold the Toeplitz condi-tion. From the point of view of numerical stability, it is not desirable. Use of Fibonacci se-quence in the ordinary differential equation extrapolation methods is suggested. The sequencehas an outstanding advantage in numerical stability as compared with other sequences.