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Title: The Methods and Error Estimations on the Second-Order Differential Equations
Other Titles: 二階微分方程式的解法及其估計
Authors: 楊壬孝
Issue Date: Jun-1987
Publisher: 國立臺灣師範大學研究發展處
Office of Research and Development
Abstract: 本文中,我們將研究下列兩種類別的二階微分方程式的之修飾解法:對於第一類型(Ⅰ)的解法,目前有套裝軟體發展,如PHASER,其中使用的方法有Euler's Method, Improved Euler's Method, 及Runge-Kutta Method。但為使解更精確,我們採用Multistep method且使用Predictor-corr-hod的技巧,通常,我們為了控制錯誤至最小,最主要是要使用每一部份的答案均應準確。因此,我們發展一修飾的解法(融合Runge-Kutta Method, Adams-Bashforth Method, Adams-Moulton Method)並適當選取一小數r(見第一部份文中演算法之步驟2)來解決此問題。對於第二類型(P)的解法通常使用打靶法及有限差分法,但為顧及穩定性,我們採用有限差分法後再加以改進。然後,我們在討論此解法具較高的精確度。
In this paper, we solve the Initial Value Problem (IVP) by a Modified Predictor-Corrector method. We can prove it has trucncation error O(h4) and it is stable. For Boundary Value Problems (BVP), Shooting method and Finite-Difference method are often used. We improve these methods and get some theorems and error estimations.
Other Identifiers: 79369990-FEEB-50F6-6980-212A2FF41D6A
Appears in Collections:師大學報

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