臺灣博碩士論文加值系統

在常微分方程初始值問題的數值解法中，邊界值方法能將初始值問題轉換成對應的線性系統。在本論文中，我們使用研究使用疊代法(iterative methods)配合relaxation factor 來解這個線性系統。我們提供一個數值逼近的方法去判斷疊代矩陣的質譜半徑(spectral radius)的性質，並估計出的relaxation factor一個收斂速度較佳的範圍。在本文的各種邊界值方法中，以廣義的梯形法的收斂性質最顯現出疊帶法的效能。

In this thesis, the matrix splitting scheme and iterative methods
with relaxation have been studied in solving the initial value
problems in odes by means of boundary value methods. In stead of
obtaining the spectral radius of the iterative matrix, we have
proposed a computational approach to determine whether the
spectral radius is within one. Moreover, a range of relaxation
factor could be estimated to provide the convergent and efficient
iterative process, especially when the extended Trapezoidal typed
of boundary value methods are implemented.

1. Introduction
2. Boundary value methods
3. Iterative processes for BVM's
4. Concluding remark

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