藉由格林函數探討變換迭代法與固定點迭代之間的關聯性

Abstract

此篇論文主要在探討變換迭代法與固定點迭代之間的關聯性。變換迭代法是一種用來處理線性或非線性問題的解析技巧，我們將其與皮卡迭代法比較。另一方面，考慮非齊次常微分方程或者是非齊次偏微分方程，格林函數是一個相當好的解決技巧，在初始值問題中，我們利用此一函數的特性去推論我們所感到興趣的關聯性。本論文的結果可以應用在邊界值問題，更進一步地，在固定點迭代的選擇上也可以嘗試其他的迭代法。

The main aim of this article is to study the correlation between the variational iteration method and fixed-point iteration. The variational iteration method is an analytical technique for linear or non-linear problems and we compare it with one fixed-point iteration called Picard iteration. On the other hand, considering inhomogeneous ordinary differential equation or inhomogeneous partial differential equation, Green's function is a technique to solve these equations. We applied its special properties to deduce this correlation for initial value problems. Our result can be applied to boundary value problems. Furthermore, the selection of fixed-point iteration can be replaced.