臺灣博碩士論文加值系統

本論文先以Adams-Bashforth-Moulton 預測、校正法，改善使用顯式有限差分法計算一維二相Stefan 問題的數值解時，計算誤差隨時間之振盪現像[6]。此外，本文亦同時探討採波前固定搭配Method of Lines 方法， 將一維單相Stefan 問題之移動交界面邊轉成固定邊界， 進而進行空間之均勻與非均勻有限差分離散化， 最後呼叫matlab 內建函數， 計算數值解。

This thesis presents the Adams-Bashforth-Moulton predictor-corrector method to overcome the oscillation of computing error vs time in the explict finite difference solution for one-dimensional two-phase Stefan problems [6]. On the other hand, the front-fixing method together with method of lines is used to compute the numerical solution of one-dimensional single-phase Stefan problems such that the moving boundary is transformed into a fixed end-point in the computation domain. After the discretization of the computational spatial domain via uniform- and nonuniform-grid finite difference formula, a syatem of ordinary differential equation is then obtained and solved by using the matlab routines.

圖目錄III
表目錄IV
摘要V
Abstract VI
符號表VII
第一章前言1
第二章數值預備知識5
2.1 Lagrange 插值公式5
2.2 非均勻網格點之有限差分公式7
2.3 Adams-Bashforth-Moulton 預測-校正法10
第三章二相Stefan 問題的數值解13
3.1 熱傳導方程14
3.2 移動邊界16
3.3 離散化之數學模型17
3.5 結果與討論22
第四章固定計算邊界法25
4.1 Method of Lines 25
4.2 座標變換25
4.3 轉換I之有限差分式32
4.4 結果與討論42
第五章結論與建議51
5.1 結論51
5.2 未來研究方向51
參考文獻52
附錄A. 第二、三兩種變換之有限差分公式53
A.1 變換II 53
A.2 變換III 58

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method, Part II-special small time starting procedure, Communications in Numerical Methods in Engineering 16 (2000) 585-593.
[6] 邱靖宏， 一維Stefan問題之有限差分解。東海大學碩士論文， 2009。